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   "cell_type": "markdown",
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    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "# Julia and DifferentialEquations.jl\n",
    "\n",
    "## Chris Rackauckas, \n",
    "\n",
    "## MIT, University of Maryland, UC Irvine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Julia's in a nutshell: it's like R/MATLAB/Python, but faster!\n",
    "\n",
    "#### But there is a lot more than that!\n",
    "\n",
    "![benchmarks](https://julialang.org/images/benchmarks.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Julia has fantastic language interopability\n",
    "\n",
    "Julia has macros and code generation tools which are utilized by interop packages for seamless integration.\n",
    "\n",
    "![interop](https://github.com/UCIDataScienceInitiative/IntroToJulia/raw/master/assets/Julia_Interop_Test.jpg-large)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Julia's Syntax is Familiar\n",
    "\n",
    "Source: Higham: An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
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   "outputs": [],
   "source": [
    "%BPATH1 Brownian path simulation\n",
    "function [t,W]=BPATH1(T,N)\n",
    "randn('state',100)\n",
    "dt = T/N;\n",
    "dW = zeros(10,N);\n",
    "W = zeros(10,N);\n",
    "\n",
    "dW(:,1) = sqrt(dt)*randn(1,10);\n",
    "W(:,1) = dW(:,1);\n",
    "\n",
    "for j = 2:N\n",
    "    dW(:,j) = sqrt(dt)*randn(1,10);\n",
    "    W(:,j) = W(:,j-1) + dW(:,j);\n",
    "end\n",
    "t = [0:dt:T-dt];\n",
    "end\n",
    "\n",
    "% In Another File...\n",
    "\n",
    "f = @() BPATH1(1,10000);\n",
    "timeit(f,2)\n",
    "[t,W] = BPATH1(1,10000);\n",
    "plot(t,W,'r-')\n",
    "xlabel('t','FontSize',16)\n",
    "ylabel('W(t)','FontSize',16,'Rotation',0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1.530038 seconds (1.99 M allocations: 155.214 MiB, 12.95% gc time)\n",
      "  0.187599 seconds (500.01 k allocations: "
     ]
    },
    {
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0x34, 0x32, 0x2c, 0x22, 0x2e, 0x2f, 0x68, 0x65, 0x6c, 0x70, 0x65, 0x72, 0x73, 0x22, 0x3a, 0x31, 0x31, 0x34, 0x37, 0x7d, 0x5d, 0x7d, 0x2c, 0x7b, 0x7d, 0x2c, 0x5b, 0x32, 0x32, 0x5d, 0x29, 0x28, 0x32, 0x32, 0x29, 0x7d, 0x29, 0x3b]\n",
       "        });\n",
       "        require(['plotly'], function(Plotly) {\n",
       "            window.Plotly = Plotly;\n",
       "        });\n",
       "    </script>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80.872 MiB, 50.71% gc time)\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Random\n",
    "function bpath(T,N)\n",
    "    Random.seed!(100)\n",
    "    dt = T/N\n",
    "    dW = zeros(10,N)\n",
    "    W = zeros(10,N)\n",
    "\n",
    "    dW[:,1] = sqrt(dt)*randn(10)\n",
    "    W[:,1] = dW[:,1]\n",
    "\n",
    "    for j = 2:N\n",
    "        dW[:,j] .= sqrt(dt)*randn(10)\n",
    "        W[:,j] .= W[:,j-1] .+ dW[:,j]\n",
    "    end\n",
    "    [0:dt:T-dt],W\n",
    "end # Translation took < 1 minute\n",
    "@time t,W = bpath(1,100000)\n",
    "@time t,W = bpath(1,100000)\n",
    "# 10x speedup over MATLAB\n",
    "using Plots; gr(fmt = :png)\n",
    "plot(t,W',color=:red,xlabel=\"t\",ylabel=\"W(t)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Julia's Syntax is Concise and Mathematical\n",
    "\n",
    "[MATLAB, Julia, Python Syntax Comparison](http://cheatsheets.quantecon.org/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Julia's Engineering and Design Tradeoffs\n",
    "\n",
    "- Type structures cannot be changed after created (less dynamism but memory layout can be optimized for)\n",
    "- All functions are JIT compiled via LLVM (interactive lags but massive runtime improvements)\n",
    "- All functions specialize on the types of arguments (more compilation but gives generic programming structures)\n",
    "- Julia is interactive (use it like MATLAB/Python/R, but makes it harder to get binaries)\n",
    "- Julia has great methods for handling mutation (more optimization opportunities like C/Fortran, but more cognative burden)\n",
    "- Julia's Base library and most packages are written in Julia (you can understand the source, but learn a new package)\n",
    "- Julia has extensive tooling for code generation and metaprogramming (concise and more optimizations, but some codes can be for experienced users)\n",
    "\n",
    "To me, this gives me a language with a lot of depth which works well for computationally-expensive scientific computing applications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Julia is about Generic Programming for Speed\n",
    "\n",
    "## Object-Oriented Programming: R/Python/C++. Centered around building representations of data\n",
    "\n",
    "## Type-Dispatch Programming: Julia. Centered around implementing the generic template of the algorithm, and letting the data type choose how to efficiently implement the algorithm\n",
    "\n",
    "### Result: algorithms and packages automatically compose in an efficient way, and using the high level abstractions of the language is a proper and efficient way to design scalable codes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "; Function f\n",
      "; Location: In[1]:1\n",
      "; Function Attrs: uwtable\n",
      "define i64 @julia_f_34741(i64, i64) #0 {\n",
      "top:\n",
      "; Function +; {\n",
      "; Location: int.jl:53\n",
      "  %2 = add i64 %1, %0\n",
      ";}\n",
      "  ret i64 %2\n",
      "}\n",
      "\n",
      "; Function f\n",
      "; Location: In[1]:1\n",
      "; Function Attrs: uwtable\n",
      "define double @julia_f_34744(double, double) #0 {\n",
      "top:\n",
      "; Function +; {\n",
      "; Location: float.jl:395\n",
      "  %2 = fadd double %0, %1\n",
      ";}\n",
      "  ret double %2\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "f(x,y) = x + y\n",
    "@code_llvm f(1,1)\n",
    "@code_llvm f(1.0,1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# DifferentialEquations.jl\n",
    "\n",
    "DifferentialEquations.jl is the core differential equation solver package in Julia. In a nutshell, it provides solvers for:\n",
    "\n",
    "- ODEs\n",
    "- DAEs\n",
    "- SODEs, SDAEs\n",
    "- Discrete stochastic (Gillespie) equations, mixed with ODEs/SDEs (jump diffusions)\n",
    "- DDEs\n",
    "- PDEs\n",
    "\n",
    "It provides wrappers to the common C++ and Fortran libraries, along with native Julia implementations with efficient genric algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Case Study: Lotka-Volterra in many ways\n",
    "\n",
    "First, the basic ODE with functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
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       "  1002.14,1077 1004.34,1072.55 1006.54,1068.03 1008.74,1063.45 1010.94,1058.8 1013.15,1054.07 1015.35,1049.28 1017.55,1044.42 1019.75,1039.49 1021.96,1034.49 \n",
       "  1024.16,1029.42 1026.36,1024.27 1028.56,1019.06 1030.76,1013.76 1032.97,1008.4 1035.17,1002.96 1037.37,997.437 1039.57,991.842 1041.77,986.169 1043.98,980.418 \n",
       "  1046.18,974.587 1048.38,968.676 1050.58,962.684 1052.79,956.611 1054.99,950.456 1057.19,944.217 1059.39,937.895 1061.59,931.489 1063.8,924.998 1066,918.421 \n",
       "  1068.2,911.758 1070.4,905.007 1072.61,898.169 1074.81,891.243 1077.01,884.228 1079.21,877.124 1081.41,869.929 1083.62,862.644 1085.82,855.267 1088.02,847.798 \n",
       "  1090.22,840.237 1092.43,832.584 1094.63,824.836 1096.83,816.994 1099.03,809.058 1101.23,801.027 1103.44,792.9 1105.64,784.677 1107.84,776.362 1110.04,767.959 \n",
       "  1112.25,759.468 1114.45,750.885 1116.65,742.21 1118.85,733.439 1121.05,724.572 1123.26,715.608 1125.46,706.545 1127.66,697.383 1129.86,688.121 1132.07,678.76 \n",
       "  1134.27,669.299 1136.47,659.739 1138.67,650.08 1140.87,640.323 1143.08,630.468 1145.28,620.518 1147.48,610.473 1149.68,600.336 1151.89,590.108 1154.09,579.792 \n",
       "  1156.29,569.39 1158.49,558.904 1160.69,548.339 1162.9,537.696 1165.1,526.98 1167.3,516.194 1169.5,505.343 1171.71,494.429 1173.91,483.458 1176.11,472.435 \n",
       "  1178.31,461.364 1180.51,450.25 1182.72,439.1 1184.92,427.918 1187.12,416.71 1189.32,405.483 1191.53,394.243 1193.73,382.996 1195.93,371.75 1198.13,360.512 \n",
       "  1200.33,349.289 1202.54,338.088 1204.74,326.917 1206.94,315.785 1209.14,304.7 1211.35,293.67 1213.55,282.701 1215.75,271.793 1217.95,260.967 1220.15,250.245 \n",
       "  1222.36,239.648 1224.56,229.201 1226.76,218.925 1228.96,208.845 1231.17,198.984 1233.37,189.365 1235.57,180.015 1237.77,170.956 1239.97,162.215 1242.18,153.817 \n",
       "  1244.38,145.787 1246.58,138.151 1248.78,130.937 1250.99,124.171 1253.19,117.879 1255.39,112.09 1257.59,106.831 1259.79,102.13 1262,98.0161 1264.2,94.5175 \n",
       "  1266.4,91.6636 1268.6,89.4837 1270.8,88.0078 1273.01,87.266 1275.21,87.2886 1277.41,88.1067 1279.61,89.7512 1281.82,92.2538 1284.02,95.6462 1286.22,99.9606 \n",
       "  1288.42,105.23 1290.62,111.486 1292.83,118.792 1295.03,127.181 1297.23,136.634 1299.43,147.128 1301.64,158.64 1303.84,171.143 1306.04,184.608 1308.24,199.005 \n",
       "  1310.44,214.301 1312.65,230.461 1314.85,247.449 1317.05,265.224 1319.25,283.747 1321.46,302.973 1323.66,322.857 1325.86,343.352 1328.06,364.407 1330.26,385.971 \n",
       "  1332.47,407.989 1334.67,430.406 1336.87,453.164 1339.07,476.202 1341.28,499.457 1343.48,522.865 1345.68,546.359 1347.88,569.87 1350.08,593.328 1352.29,616.658 \n",
       "  1354.49,639.786 1356.69,662.635 1358.89,685.129 1361.1,707.259 1363.3,729.003 1365.5,750.329 1367.7,771.208 1369.9,791.613 1372.11,811.522 1374.31,830.912 \n",
       "  1376.51,849.767 1378.71,868.071 1380.92,885.812 1383.12,902.979 1385.32,919.567 1387.52,935.57 1389.72,950.989 1391.93,965.823 1394.13,980.078 1396.33,993.761 \n",
       "  1398.53,1006.88 1400.74,1019.45 1402.94,1031.49 1405.14,1043.01 1407.34,1054.03 1409.54,1064.59 1411.75,1074.7 1413.95,1084.39 1416.15,1093.7 1418.35,1102.66 \n",
       "  1420.56,1111.25 1422.76,1119.46 1424.96,1127.31 1427.16,1134.8 1429.36,1141.95 1431.57,1148.79 1433.77,1155.31 1435.97,1161.53 1438.17,1167.47 1440.38,1173.13 \n",
       "  1442.58,1178.54 1444.78,1183.69 1446.98,1188.6 1449.18,1193.28 1451.39,1197.74 1453.59,1201.98 1455.79,1206.02 1457.99,1209.87 1460.2,1213.53 1462.4,1217.01 \n",
       "  1464.6,1220.31 1466.8,1223.45 1469,1226.42 1471.21,1229.24 1473.41,1231.91 1475.61,1234.43 1477.81,1236.81 1480.02,1239.05 1482.22,1241.18 1484.42,1243.18 \n",
       "  1486.62,1245.07 1488.82,1246.84 1491.03,1248.5 1493.23,1250.06 1495.43,1251.52 1497.63,1252.88 1499.83,1254.14 1502.04,1255.31 1504.24,1256.4 1506.44,1257.39 \n",
       "  1508.64,1258.31 1510.85,1259.14 1513.05,1259.89 1515.25,1260.57 1517.45,1261.18 1519.65,1261.71 1521.86,1262.17 1524.06,1262.57 1526.26,1262.9 1528.46,1263.17 \n",
       "  1530.67,1263.37 1532.87,1263.52 1535.07,1263.6 1537.27,1263.62 1539.47,1263.59 1541.68,1263.5 1543.88,1263.35 1546.08,1263.15 1548.28,1262.89 1550.49,1262.59 \n",
       "  1552.69,1262.23 1554.89,1261.82 1557.09,1261.36 1559.29,1260.85 1561.5,1260.29 1563.7,1259.68 1565.9,1259.02 1568.1,1258.32 1570.31,1257.57 1572.51,1256.77 \n",
       "  1574.71,1255.93 1576.91,1255.03 1579.11,1254.1 1581.32,1253.12 1583.52,1252.09 1585.72,1251.02 1587.92,1249.91 1590.13,1248.75 1592.33,1247.55 1594.53,1246.3 \n",
       "  1596.73,1245.01 1598.93,1243.68 1601.14,1242.31 1603.34,1240.89 1605.54,1239.43 1607.74,1237.92 1609.95,1236.37 1612.15,1234.78 1614.35,1233.15 1616.55,1231.47 \n",
       "  1618.75,1229.75 1620.96,1227.99 1623.16,1226.18 1625.36,1224.33 1627.56,1222.43 1629.77,1220.49 1631.97,1218.51 1634.17,1216.48 1636.37,1214.41 1638.57,1212.29 \n",
       "  1640.78,1210.12 1642.98,1207.91 1645.18,1205.66 1647.38,1203.36 1649.59,1201.01 1651.79,1198.62 1653.99,1196.17 1656.19,1193.69 1658.39,1191.15 1660.6,1188.56 \n",
       "  1662.8,1185.93 1665,1183.25 1667.2,1180.52 1669.41,1177.74 1671.61,1174.91 1673.81,1172.03 1676.01,1169.1 1678.21,1166.12 1680.42,1163.08 1682.62,1160 \n",
       "  1684.82,1156.86 1687.02,1153.67 1689.23,1150.42 1691.43,1147.12 1693.63,1143.77 1695.83,1140.36 1698.03,1136.9 1700.24,1133.38 1702.44,1129.8 1704.64,1126.17 \n",
       "  1706.84,1122.48 1709.05,1118.73 1711.25,1114.92 1713.45,1111.05 1715.65,1107.12 1717.85,1103.13 1720.06,1099.08 1722.26,1094.96 1724.46,1090.79 1726.66,1086.55 \n",
       "  1728.86,1082.24 1731.07,1077.88 1733.27,1073.44 1735.47,1068.94 1737.67,1064.38 1739.88,1059.74 1742.08,1055.04 1744.28,1050.27 1746.48,1045.43 1748.68,1040.53 \n",
       "  1750.89,1035.55 1753.09,1030.49 1755.29,1025.37 1757.49,1020.18 1759.7,1014.91 1761.9,1009.56 1764.1,1004.14 1766.3,998.65 1768.5,993.079 1770.71,987.431 \n",
       "  1772.91,981.705 1775.11,975.9 1777.31,970.016 1779.52,964.051 1781.72,958.006 1783.92,951.878 1786.12,945.668 1788.32,939.374 1790.53,932.997 1792.73,926.535 \n",
       "  1794.93,919.99 1797.13,913.359 1799.34,906.642 1801.54,899.837 1803.74,892.945 1805.94,885.964 1808.14,878.893 1810.35,871.731 1812.55,864.478 1814.75,857.134 \n",
       "  1816.95,849.696 1819.16,842.166 1821.36,834.543 1823.56,826.825 1825.76,819.013 1827.96,811.106 1830.17,803.104 1832.37,795.007 1834.57,786.814 1836.77,778.525 \n",
       "  1838.98,770.14 1841.18,761.659 1843.38,753.083 1845.58,744.41 1847.78,735.641 1849.99,726.777 1852.19,717.816 1854.39,708.761 1856.59,699.61 1858.8,690.364 \n",
       "  1861,681.024 1863.2,671.59 1865.4,662.061 1867.6,652.44 1869.81,642.726 1872.01,632.92 1874.21,623.023 1876.41,613.035 1878.62,602.968 1880.82,592.833 \n",
       "  1883.02,582.626 1885.22,572.345 1887.42,561.988 1889.63,551.554 1891.83,541.042 1894.03,530.453 1896.23,519.787 1898.44,509.046 1900.64,498.232 1902.84,487.347 \n",
       "  1905.04,476.394 1907.24,465.378 1909.45,454.303 1911.65,443.174 1913.85,431.996 1916.05,420.777 1918.26,409.523 1920.46,398.242 1922.66,386.942 1924.86,375.633 \n",
       "  1927.06,364.322 1929.27,353.022 1931.47,341.742 1933.67,330.495 1935.87,319.291 1938.08,308.144 1940.28,297.067 1942.48,286.074 1944.68,275.18 1946.88,264.399 \n",
       "  1949.09,253.748 1951.29,243.243 1953.49,232.901 1955.69,222.74 1957.89,212.779 1960.1,203.035 1962.3,193.529 1964.5,184.281 1966.7,175.311 1968.91,166.642 \n",
       "  1971.11,158.295 1973.31,150.294 1975.51,142.661 1977.71,135.42 1979.92,128.597 1982.12,122.215 1984.32,116.303 1986.52,110.884 1988.73,105.987 1990.93,101.641 \n",
       "  1993.13,97.891 1995.33,94.7822 1997.53,92.3563 1999.74,90.6522 2001.94,89.7062 2004.14,89.552 2006.34,90.2206 2008.55,91.7401 2010.75,94.136 2012.95,97.4311 \n",
       "  2015.15,101.646 2017.35,106.797 2019.56,112.899 2021.76,119.965 2023.96,128.003 2026.16,137.02 2028.37,147.02 2030.57,158.005 2032.77,169.971 2034.97,182.916 \n",
       "  2037.17,196.832 2039.38,211.709 2041.58,227.546 2043.78,244.314 2045.98,261.953 2048.19,280.402 2050.39,299.601 2052.59,319.49 2054.79,340.006 2056.99,361.09 \n",
       "  2059.2,382.68 2061.4,404.714 2063.6,427.133 2065.8,449.872 2068.01,472.872 2070.21,496.069 2072.41,519.402 2074.61,542.808 2076.81,566.225 2079.02,589.59 \n",
       "  2081.22,612.84 2083.42,635.912 2085.62,658.744 2087.83,681.271 2090.03,703.43 2092.23,725.181 2094.43,746.508 2096.63,767.385 2098.84,787.789 2101.04,807.697 \n",
       "  2103.24,827.093 2105.44,845.958 2107.65,864.281 2109.85,882.049 2112.05,899.255 2114.25,915.891 2116.45,931.955 2118.66,947.446 2120.86,962.364 2123.06,976.715 \n",
       "  2125.26,990.504 2127.47,1003.74 2129.67,1016.43 2131.87,1028.6 2134.07,1040.26 2136.27,1051.43 2138.48,1062.12 2140.68,1072.37 2142.88,1082.21 2145.08,1091.65 \n",
       "  2147.29,1100.71 2149.49,1109.37 2151.69,1117.64 2153.89,1125.55 2156.09,1133.11 2158.3,1140.32 2160.5,1147.21 2162.7,1153.79 2164.9,1160.07 2167.11,1166.06 \n",
       "  2169.31,1171.78 2171.51,1177.23 2173.71,1182.42 2175.91,1187.38 2178.12,1192.1 2180.32,1196.59 2182.52,1200.88 2184.72,1204.95 2186.92,1208.83 2189.13,1212.51 \n",
       "  2191.33,1216.02 2193.53,1219.34 2195.73,1222.49 2197.94,1225.48 2200.14,1228.32 2202.34,1231 2204.54,1233.55 2206.74,1235.96 2208.95,1238.23 2211.15,1240.38 \n",
       "  2213.35,1242.4 2215.55,1244.31 2217.76,1246.1 2219.96,1247.79 2222.16,1249.36 2224.36,1250.84 2226.56,1252.22 2228.77,1253.5 2230.97,1254.69 2233.17,1255.79 \n",
       "  2235.37,1256.8 2237.58,1257.73 2239.78,1258.58 2241.98,1259.35 2244.18,1260.05 2246.38,1260.67 2248.59,1261.23 2250.79,1261.71 2252.99,1262.12 2255.19,1262.46 \n",
       "  2257.4,1262.74 2259.6,1262.96 2261.8,1263.11 2264,1263.21 2266.2,1263.24 2268.41,1263.22 2270.61,1263.14 2272.81,1263 2275.01,1262.81 2277.22,1262.57 \n",
       "  2279.42,1262.27 2281.62,1261.92 2283.82,1261.51 2286.02,1261.06 2288.23,1260.56 2290.43,1260 2292.63,1259.4 2294.83,1258.75 2297.04,1258.06 2299.24,1257.31 \n",
       "  2301.44,1256.52 2303.64,1255.68 2305.84,1254.8 2308.05,1253.87 2310.25,1252.9 2312.45,1251.88 2314.65,1250.82 2316.86,1249.72 2319.06,1248.57 2321.26,1247.37 \n",
       "  \n",
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       "  143.273,1289.47 145.475,1292.59 147.677,1295.63 149.879,1298.61 152.081,1301.51 154.284,1304.35 156.486,1307.12 158.688,1309.83 160.89,1312.48 163.093,1315.06 \n",
       "  165.295,1317.59 167.497,1320.05 169.699,1322.46 171.901,1324.81 174.104,1327.11 176.306,1329.35 178.508,1331.54 180.71,1333.67 182.912,1335.76 185.115,1337.79 \n",
       "  187.317,1339.78 189.519,1341.72 191.721,1343.62 193.924,1345.46 196.126,1347.27 198.328,1349.03 200.53,1350.75 202.732,1352.42 204.935,1354.06 207.137,1355.65 \n",
       "  209.339,1357.21 211.541,1358.73 213.743,1360.21 215.946,1361.65 218.148,1363.06 220.35,1364.43 222.552,1365.77 224.754,1367.07 226.957,1368.34 229.159,1369.58 \n",
       "  231.361,1370.79 233.563,1371.96 235.766,1373.11 237.968,1374.22 240.17,1375.31 242.372,1376.37 244.574,1377.4 246.777,1378.4 248.979,1379.37 251.181,1380.32 \n",
       "  253.383,1381.24 255.585,1382.14 257.788,1383.01 259.99,1383.86 262.192,1384.68 264.394,1385.48 266.596,1386.26 268.799,1387.01 271.001,1387.74 273.203,1388.45 \n",
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       "  297.427,1394.85 299.63,1395.32 301.832,1395.76 304.034,1396.19 306.236,1396.6 308.439,1396.99 310.641,1397.36 312.843,1397.71 315.045,1398.05 317.247,1398.36 \n",
       "  319.45,1398.66 321.652,1398.95 323.854,1399.21 326.056,1399.46 328.258,1399.69 330.461,1399.9 332.663,1400.09 334.865,1400.27 337.067,1400.43 339.269,1400.57 \n",
       "  341.472,1400.69 343.674,1400.8 345.876,1400.89 348.078,1400.95 350.281,1401 352.483,1401.04 354.685,1401.05 356.887,1401.05 359.089,1401.02 361.292,1400.98 \n",
       "  363.494,1400.92 365.696,1400.83 367.898,1400.73 370.1,1400.61 372.303,1400.46 374.505,1400.29 376.707,1400.11 378.909,1399.89 381.111,1399.66 383.314,1399.4 \n",
       "  385.516,1399.12 387.718,1398.81 389.92,1398.48 392.123,1398.12 394.325,1397.73 396.527,1397.32 398.729,1396.87 400.931,1396.4 403.134,1395.89 405.336,1395.35 \n",
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       "  473.604,1353.42 475.807,1350.74 478.009,1347.94 480.211,1345.01 482.413,1341.95 484.615,1338.74 486.818,1335.39 489.02,1331.86 491.222,1328.16 493.424,1324.27 \n",
       "  495.626,1320.17 497.829,1315.87 500.031,1311.33 502.233,1306.56 504.435,1301.54 506.638,1296.26 508.84,1290.71 511.042,1284.88 513.244,1278.75 515.446,1272.33 \n",
       "  517.649,1265.59 519.851,1258.52 522.053,1251.13 524.255,1243.39 526.457,1235.3 528.66,1226.84 530.862,1218.01 533.064,1208.8 535.266,1199.2 537.469,1189.19 \n",
       "  539.671,1178.78 541.873,1167.95 544.075,1156.69 546.277,1144.99 548.48,1132.85 550.682,1120.26 552.884,1107.2 555.086,1093.68 557.288,1079.67 559.491,1065.18 \n",
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       "  605.737,707.622 607.939,692.161 610.141,677.25 612.344,662.945 614.546,649.304 616.748,636.385 618.95,624.25 621.153,612.936 623.355,602.449 625.557,592.814 \n",
       "  627.759,584.052 629.961,576.183 632.164,569.219 634.366,563.17 636.568,558.043 638.77,553.84 640.972,550.557 643.175,548.19 645.377,546.726 647.579,546.153 \n",
       "  649.781,546.451 651.984,547.598 654.186,549.568 656.388,552.329 658.59,555.847 660.792,560.084 662.995,564.996 665.197,570.537 667.399,576.656 669.601,583.298 \n",
       "  671.803,590.403 674.006,597.909 676.208,605.806 678.41,614.105 680.612,622.773 682.814,631.779 685.017,641.09 687.219,650.678 689.421,660.513 691.623,670.569 \n",
       "  693.826,680.818 696.028,691.237 698.23,701.8 700.432,712.486 702.634,723.273 704.837,734.14 707.039,745.068 709.241,756.04 711.443,767.037 713.645,778.046 \n",
       "  715.848,789.05 718.05,800.038 720.252,810.996 722.454,821.913 724.656,832.781 726.859,843.588 729.061,854.318 731.263,864.964 733.465,875.519 735.668,885.979 \n",
       "  737.87,896.337 740.072,906.589 742.274,916.729 744.476,926.754 746.679,936.658 748.881,946.439 751.083,956.092 753.285,965.615 755.487,975.005 757.69,984.259 \n",
       "  759.892,993.375 762.094,1002.35 764.296,1011.19 766.499,1019.88 768.701,1028.43 770.903,1036.83 773.105,1045.1 775.307,1053.21 777.51,1061.19 779.712,1069.02 \n",
       "  781.914,1076.71 784.116,1084.25 786.318,1091.67 788.521,1098.94 790.723,1106.08 792.925,1113.08 795.127,1119.95 797.329,1126.68 799.532,1133.28 801.734,1139.75 \n",
       "  803.936,1146.1 806.138,1152.31 808.341,1158.4 810.543,1164.37 812.745,1170.21 814.947,1175.93 817.149,1181.54 819.352,1187.02 821.554,1192.4 823.756,1197.65 \n",
       "  825.958,1202.8 828.16,1207.84 830.363,1212.76 832.565,1217.59 834.767,1222.3 836.969,1226.92 839.171,1231.43 841.374,1235.85 843.576,1240.17 845.778,1244.39 \n",
       "  847.98,1248.52 850.183,1252.55 852.385,1256.5 854.587,1260.36 856.789,1264.13 858.991,1267.82 861.194,1271.43 863.396,1274.95 865.598,1278.4 867.8,1281.76 \n",
       "  870.002,1285.05 872.205,1288.27 874.407,1291.41 876.609,1294.48 878.811,1297.48 881.014,1300.41 883.216,1303.27 885.418,1306.07 887.62,1308.8 889.822,1311.47 \n",
       "  892.025,1314.08 894.227,1316.63 896.429,1319.11 898.631,1321.54 900.833,1323.91 903.036,1326.23 905.238,1328.49 907.44,1330.7 909.642,1332.86 911.844,1334.96 \n",
       "  914.047,1337.02 916.249,1339.03 918.451,1340.99 920.653,1342.9 922.856,1344.76 925.058,1346.58 927.26,1348.36 929.462,1350.1 931.664,1351.79 933.867,1353.44 \n",
       "  936.069,1355.05 938.271,1356.62 940.473,1358.15 942.675,1359.64 944.878,1361.1 947.08,1362.52 949.282,1363.9 951.484,1365.25 953.686,1366.56 955.889,1367.85 \n",
       "  958.091,1369.1 960.293,1370.31 962.495,1371.5 964.698,1372.65 966.9,1373.78 969.102,1374.88 971.304,1375.94 973.506,1376.98 975.709,1377.99 977.911,1378.98 \n",
       "  980.113,1379.94 982.315,1380.87 984.517,1381.77 986.72,1382.65 988.922,1383.51 991.124,1384.34 993.326,1385.15 995.529,1385.94 997.731,1386.7 999.933,1387.44 \n",
       "  1002.14,1388.15 1004.34,1388.85 1006.54,1389.52 1008.74,1390.17 1010.94,1390.8 1013.15,1391.41 1015.35,1392 1017.55,1392.57 1019.75,1393.12 1021.96,1393.65 \n",
       "  1024.16,1394.16 1026.36,1394.65 1028.56,1395.12 1030.76,1395.57 1032.97,1396 1035.17,1396.42 1037.37,1396.81 1039.57,1397.19 1041.77,1397.55 1043.98,1397.89 \n",
       "  1046.18,1398.21 1048.38,1398.52 1050.58,1398.81 1052.79,1399.08 1054.99,1399.33 1057.19,1399.57 1059.39,1399.79 1061.59,1399.99 1063.8,1400.17 1066,1400.34 \n",
       "  1068.2,1400.49 1070.4,1400.62 1072.61,1400.73 1074.81,1400.82 1077.01,1400.9 1079.21,1400.96 1081.41,1401 1083.62,1401.02 1085.82,1401.02 1088.02,1401 \n",
       "  1090.22,1400.96 1092.43,1400.91 1094.63,1400.83 1096.83,1400.73 1099.03,1400.61 1101.23,1400.48 1103.44,1400.32 1105.64,1400.13 1107.84,1399.93 1110.04,1399.69 \n",
       "  1112.25,1399.43 1114.45,1399.14 1116.65,1398.82 1118.85,1398.48 1121.05,1398.1 1123.26,1397.71 1125.46,1397.28 1127.66,1396.83 1129.86,1396.35 1132.07,1395.84 \n",
       "  1134.27,1395.31 1136.47,1394.74 1138.67,1394.15 1140.87,1393.52 1143.08,1392.86 1145.28,1392.16 1147.48,1391.43 1149.68,1390.66 1151.89,1389.85 1154.09,1389 \n",
       "  1156.29,1388.11 1158.49,1387.17 1160.69,1386.19 1162.9,1385.15 1165.1,1384.06 1167.3,1382.92 1169.5,1381.71 1171.71,1380.45 1173.91,1379.12 1176.11,1377.72 \n",
       "  1178.31,1376.25 1180.51,1374.71 1182.72,1373.09 1184.92,1371.38 1187.12,1369.59 1189.32,1367.71 1191.53,1365.73 1193.73,1363.66 1195.93,1361.48 1198.13,1359.19 \n",
       "  1200.33,1356.79 1202.54,1354.27 1204.74,1351.62 1206.94,1348.85 1209.14,1345.95 1211.35,1342.9 1213.55,1339.72 1215.75,1336.4 1217.95,1332.92 1220.15,1329.28 \n",
       "  1222.36,1325.47 1224.56,1321.46 1226.76,1317.24 1228.96,1312.81 1231.17,1308.14 1233.37,1303.23 1235.57,1298.07 1237.77,1292.63 1239.97,1286.92 1242.18,1280.91 \n",
       "  1244.38,1274.6 1246.58,1267.98 1248.78,1261.04 1250.99,1253.76 1253.19,1246.13 1255.39,1238.15 1257.59,1229.81 1259.79,1221.09 1262,1212 1264.2,1202.51 \n",
       "  1266.4,1192.62 1268.6,1182.33 1270.8,1171.62 1273.01,1160.49 1275.21,1148.94 1277.41,1136.94 1279.61,1124.5 1281.82,1111.61 1284.02,1098.27 1286.22,1084.47 \n",
       "  1288.42,1070.19 1290.62,1055.45 1292.83,1040.19 1295.03,1024.39 1297.23,1008.13 1299.43,991.453 1301.64,974.419 1303.84,957.085 1306.04,939.507 1308.24,921.741 \n",
       "  1310.44,903.841 1312.65,885.861 1314.85,867.857 1317.05,849.879 1319.25,831.982 1321.46,814.217 1323.66,796.636 1325.86,779.29 1328.06,762.229 1330.26,745.502 \n",
       "  1332.47,729.159 1334.67,713.249 1336.87,697.819 1339.07,682.917 1341.28,668.591 1343.48,654.885 1345.68,641.847 1347.88,629.521 1350.08,617.952 1352.29,607.183 \n",
       "  1354.49,597.259 1356.69,588.223 1358.89,580.113 1361.1,572.93 1363.3,566.663 1365.5,561.31 1367.7,556.863 1369.9,553.313 1372.11,550.649 1374.31,548.859 \n",
       "  1376.51,547.927 1378.71,547.835 1380.92,548.565 1383.12,550.096 1385.32,552.403 1387.52,555.461 1389.72,559.243 1391.93,563.718 1394.13,568.856 1396.33,574.622 \n",
       "  1398.53,580.98 1400.74,587.893 1402.94,595.319 1405.14,603.217 1407.34,611.542 1409.54,620.249 1411.75,629.288 1413.95,638.61 1416.15,648.16 1418.35,657.887 \n",
       "  1420.56,667.806 1422.76,677.924 1424.96,688.217 1427.16,698.664 1429.36,709.242 1431.57,719.93 1433.77,730.71 1435.97,741.561 1438.17,752.466 1440.38,763.408 \n",
       "  1442.58,774.37 1444.78,785.337 1446.98,796.295 1449.18,807.231 1451.39,818.13 1453.59,828.982 1455.79,839.776 1457.99,850.502 1460.2,861.151 1462.4,871.714 \n",
       "  1464.6,882.185 1466.8,892.556 1469,902.824 1471.21,912.982 1473.41,923.027 1475.61,932.957 1477.81,942.766 1480.02,952.447 1482.22,961.996 1484.42,971.412 \n",
       "  1486.62,980.693 1488.82,989.838 1491.03,998.846 1493.23,1007.72 1495.43,1016.45 1497.63,1025.04 1499.83,1033.49 1502.04,1041.8 1504.24,1049.96 1506.44,1057.99 \n",
       "  1508.64,1065.88 1510.85,1073.62 1513.05,1081.23 1515.25,1088.69 1517.45,1096.01 1519.65,1103.2 1521.86,1110.25 1524.06,1117.16 1526.26,1123.94 1528.46,1130.58 \n",
       "  1530.67,1137.1 1532.87,1143.48 1535.07,1149.73 1537.27,1155.86 1539.47,1161.86 1541.68,1167.75 1543.88,1173.51 1546.08,1179.16 1548.28,1184.68 1550.49,1190.09 \n",
       "  1552.69,1195.39 1554.89,1200.57 1557.09,1205.65 1559.29,1210.61 1561.5,1215.47 1563.7,1220.23 1565.9,1224.88 1568.1,1229.43 1570.31,1233.89 1572.51,1238.24 \n",
       "  1574.71,1242.5 1576.91,1246.67 1579.11,1250.74 1581.32,1254.72 1583.52,1258.62 1585.72,1262.43 1587.92,1266.15 1590.13,1269.79 1592.33,1273.34 1594.53,1276.82 \n",
       "  1596.73,1280.22 1598.93,1283.54 1601.14,1286.78 1603.34,1289.95 1605.54,1293.05 1607.74,1296.07 1609.95,1299.03 1612.15,1301.92 1614.35,1304.74 1616.55,1307.5 \n",
       "  1618.75,1310.19 1620.96,1312.82 1623.16,1315.39 1625.36,1317.9 1627.56,1320.35 1629.77,1322.74 1631.97,1325.08 1634.17,1327.36 1636.37,1329.59 1638.57,1331.77 \n",
       "  1640.78,1333.89 1642.98,1335.96 1645.18,1337.99 1647.38,1339.96 1649.59,1341.89 1651.79,1343.78 1653.99,1345.61 1656.19,1347.41 1658.39,1349.16 1660.6,1350.87 \n",
       "  1662.8,1352.53 1665,1354.16 1667.2,1355.75 1669.41,1357.3 1671.61,1358.81 1673.81,1360.28 1676.01,1361.72 1678.21,1363.12 1680.42,1364.48 1682.62,1365.81 \n",
       "  1684.82,1367.11 1687.02,1368.38 1689.23,1369.61 1691.43,1370.81 1693.63,1371.98 1695.83,1373.12 1698.03,1374.23 1700.24,1375.31 1702.44,1376.36 1704.64,1377.38 \n",
       "  1706.84,1378.38 1709.05,1379.35 1711.25,1380.29 1713.45,1381.2 1715.65,1382.09 1717.85,1382.96 1720.06,1383.8 1722.26,1384.61 1724.46,1385.41 1726.66,1386.17 \n",
       "  1728.86,1386.92 1731.07,1387.64 1733.27,1388.34 1735.47,1389.02 1737.67,1389.68 1739.88,1390.32 1742.08,1390.94 1744.28,1391.53 1746.48,1392.11 1748.68,1392.66 \n",
       "  1750.89,1393.2 1753.09,1393.71 1755.29,1394.21 1757.49,1394.69 1759.7,1395.15 1761.9,1395.59 1764.1,1396.01 1766.3,1396.41 1768.5,1396.8 1770.71,1397.16 \n",
       "  1772.91,1397.51 1775.11,1397.84 1777.31,1398.16 1779.52,1398.45 1781.72,1398.73 1783.92,1398.99 1786.12,1399.23 1788.32,1399.45 1790.53,1399.66 1792.73,1399.85 \n",
       "  1794.93,1400.02 1797.13,1400.17 1799.34,1400.3 1801.54,1400.41 1803.74,1400.51 1805.94,1400.59 1808.14,1400.65 1810.35,1400.69 1812.55,1400.72 1814.75,1400.72 \n",
       "  1816.95,1400.71 1819.16,1400.67 1821.36,1400.62 1823.56,1400.55 1825.76,1400.46 1827.96,1400.35 1830.17,1400.22 1832.37,1400.06 1834.57,1399.89 1836.77,1399.69 \n",
       "  1838.98,1399.47 1841.18,1399.23 1843.38,1398.96 1845.58,1398.67 1847.78,1398.35 1849.99,1398 1852.19,1397.63 1854.39,1397.23 1856.59,1396.81 1858.8,1396.35 \n",
       "  1861,1395.86 1863.2,1395.34 1865.4,1394.79 1867.6,1394.21 1869.81,1393.59 1872.01,1392.93 1874.21,1392.24 1876.41,1391.51 1878.62,1390.74 1880.82,1389.91 \n",
       "  1883.02,1389.03 1885.22,1388.11 1887.42,1387.13 1889.63,1386.11 1891.83,1385.03 1894.03,1383.9 1896.23,1382.71 1898.44,1381.47 1900.64,1380.17 1902.84,1378.82 \n",
       "  1905.04,1377.4 1907.24,1375.91 1909.45,1374.36 1911.65,1372.73 1913.85,1371.03 1916.05,1369.25 1918.26,1367.39 1920.46,1365.43 1922.66,1363.39 1924.86,1361.25 \n",
       "  1927.06,1359 1929.27,1356.64 1931.47,1354.17 1933.67,1351.58 1935.87,1348.86 1938.08,1346 1940.28,1343 1942.48,1339.85 1944.68,1336.55 1946.88,1333.08 \n",
       "  1949.09,1329.43 1951.29,1325.6 1953.49,1321.58 1955.69,1317.36 1957.89,1312.93 1960.1,1308.28 1962.3,1303.4 1964.5,1298.29 1966.7,1292.91 1968.91,1287.28 \n",
       "  1971.11,1281.38 1973.31,1275.19 1975.51,1268.7 1977.71,1261.9 1979.92,1254.79 1982.12,1247.34 1984.32,1239.54 1986.52,1231.39 1988.73,1222.86 1990.93,1213.96 \n",
       "  1993.13,1204.66 1995.33,1194.94 1997.53,1184.8 1999.74,1174.23 2001.94,1163.2 2004.14,1151.72 2006.34,1139.78 2008.55,1127.39 2010.75,1114.53 2012.95,1101.21 \n",
       "  2015.15,1087.45 2017.35,1073.24 2019.56,1058.6 2021.76,1043.54 2023.96,1028.08 2026.16,1012.24 2028.37,996.035 2030.57,979.49 2032.77,962.631 2034.97,945.487 \n",
       "  2037.17,928.088 2039.38,910.47 2041.58,892.659 2043.78,874.708 2045.98,856.69 2048.19,838.675 2050.39,820.732 2052.59,802.928 2054.79,785.328 2056.99,767.992 \n",
       "  2059.2,750.982 2061.4,734.356 2063.6,718.168 2065.8,702.473 2068.01,687.323 2070.21,672.765 2072.41,658.849 2074.61,645.618 2076.81,633.115 2079.02,621.381 \n",
       "  2081.22,610.455 2083.42,600.373 2085.62,591.168 2087.83,582.874 2090.03,575.519 2092.23,569.113 2094.43,563.638 2096.63,559.082 2098.84,555.431 2101.04,552.671 \n",
       "  2103.24,550.785 2105.44,549.755 2107.65,549.561 2109.85,550.182 2112.05,551.594 2114.25,553.773 2116.45,556.692 2118.66,560.323 2120.86,564.637 2123.06,569.602 \n",
       "  2125.26,575.186 2127.47,581.354 2129.67,588.069 2131.87,595.293 2134.07,602.988 2136.27,611.113 2138.48,619.623 2140.68,628.476 2142.88,637.625 2145.08,647.022 \n",
       "  2147.29,656.646 2149.49,666.505 2151.69,676.571 2153.89,686.82 2156.09,697.229 2158.3,707.775 2160.5,718.436 2162.7,729.192 2164.9,740.022 2167.11,750.909 \n",
       "  2169.31,761.835 2171.51,772.782 2173.71,783.736 2175.91,794.682 2178.12,805.606 2180.32,816.495 2182.52,827.339 2184.72,838.125 2186.92,848.846 2189.13,859.491 \n",
       "  2191.33,870.054 2193.53,880.528 2195.73,890.907 2197.94,901.187 2200.14,911.358 2202.34,921.414 2204.54,931.35 2206.74,941.163 2208.95,950.852 2211.15,960.412 \n",
       "  2213.35,969.842 2215.55,979.139 2217.76,988.302 2219.96,997.328 2222.16,1006.22 2224.36,1014.97 2226.56,1023.57 2228.77,1032.04 2230.97,1040.37 2233.17,1048.55 \n",
       "  2235.37,1056.59 2237.58,1064.49 2239.78,1072.25 2241.98,1079.87 2244.18,1087.34 2246.38,1094.68 2248.59,1101.88 2250.79,1108.94 2252.99,1115.87 2255.19,1122.66 \n",
       "  2257.4,1129.33 2259.6,1135.86 2261.8,1142.26 2264,1148.54 2266.2,1154.69 2268.41,1160.71 2270.61,1166.62 2272.81,1172.4 2275.01,1178.06 2277.22,1183.6 \n",
       "  2279.42,1189.03 2281.62,1194.35 2283.82,1199.55 2286.02,1204.64 2288.23,1209.63 2290.43,1214.51 2292.63,1219.28 2294.83,1223.95 2297.04,1228.52 2299.24,1232.98 \n",
       "  2301.44,1237.35 2303.64,1241.63 2305.84,1245.81 2308.05,1249.89 2310.25,1253.89 2312.45,1257.8 2314.65,1261.62 2316.86,1265.35 2319.06,1269 2321.26,1272.57 \n",
       "  \n",
       "  \"/>\n",
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       "1910.3,312.204 2249.26,312.204 2249.26,130.764 1910.3,130.764 \n",
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       "<polyline clip-path=\"url(#clip8801)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1910.3,312.204 2249.26,312.204 2249.26,130.764 1910.3,130.764 1910.3,312.204 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip8801)\" style=\"stroke:#009af9; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  1934.3,191.244 2078.3,191.244 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip8801)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:start;\" transform=\"rotate(0, 2102.3, 208.744)\" x=\"2102.3\" y=\"208.744\">u1(t)</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip8801)\" style=\"stroke:#e26f46; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  1934.3,251.724 2078.3,251.724 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip8801)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:start;\" transform=\"rotate(0, 2102.3, 269.224)\" x=\"2102.3\" y=\"269.224\">u2(t)</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DifferentialEquations\n",
    "function f(du,u,p,t)\n",
    "  x, y = u\n",
    "  α,β,γ,δ = p\n",
    "  du[1] = α*x - β*x*y\n",
    "  du[2] = -γ*y + δ*x*y\n",
    "end\n",
    "p = (1.5,1.0,3.0,1.0); u0 = [1.0;1.0]\n",
    "tspan = (0.0,10.0)\n",
    "prob1 = ODEProblem(f,u0,tspan,p)\n",
    "sol = solve(prob1)\n",
    "using Plots; plot(sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## DSLs and Metaprogramming for Syntactic Sugar\n",
    "\n",
    "Now let's use a DSL defined by a macro:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "f = @ode_def LotkaVolterra begin\n",
    "  dx  = α*x  - β*x*y\n",
    "  dy = -γ*y + δ*x*y\n",
    "end α β γ δ\n",
    "\n",
    "f = @ode_def LotkaVolterra begin\n",
    "  d🐁  = α*🐁 - β*🐁*🐈\n",
    "  d🐈 = -γ*🐈 + δ*🐁*🐈\n",
    "end α β γ δ\n",
    "\n",
    "sir_model = @reaction_network SIR begin\n",
    "    c1, s + i --> 2i\n",
    "    c2, i --> r\n",
    "end c1 c2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Using Generic Algorithms for Optimizations\n",
    "\n",
    "Let's specialize the speed of the integrator for small array equations by utilizing static arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "using StaticArrays\n",
    "static_u0 = @SVector [1.0,1.0]\n",
    "function f2(u,p,t)\n",
    "  x, y = u\n",
    "  α,β,γ,δ = p\n",
    "  @SVector [α*x - β*x*y, -γ*y + δ*x*y]\n",
    "end\n",
    "prob2 = ODEProblem(f2,static_u0,tspan,p)\n",
    "sol = solve(prob2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  66.47 KiB\n",
       "  allocs estimate:  509\n",
       "  --------------\n",
       "  minimum time:     64.944 μs (0.00% GC)\n",
       "  median time:      123.846 μs (0.00% GC)\n",
       "  mean time:        166.556 μs (11.31% GC)\n",
       "  maximum time:     9.024 ms (95.28% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "@benchmark solve(prob1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  66.83 KiB\n",
       "  allocs estimate:  243\n",
       "  --------------\n",
       "  minimum time:     48.330 μs (0.00% GC)\n",
       "  median time:      88.355 μs (0.00% GC)\n",
       "  mean time:        116.859 μs (10.88% GC)\n",
       "  maximum time:     8.732 ms (96.34% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark solve(prob2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Optimize the Solver By Choosing from the Largest Set of Methods\n",
    "\n",
    "http://docs.juliadiffeq.org/latest/solvers/ode_solve.html\n",
    "\n",
    "https://github.com/JuliaDiffEq/DiffEqBenchmarks.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  56.77 KiB\n",
       "  allocs estimate:  119\n",
       "  --------------\n",
       "  minimum time:     22.656 μs (0.00% GC)\n",
       "  median time:      49.840 μs (0.00% GC)\n",
       "  mean time:        62.234 μs (14.02% GC)\n",
       "  maximum time:     4.155 ms (97.28% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark solve(prob2,Vern9())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  63.77 KiB\n",
       "  allocs estimate:  765\n",
       "  --------------\n",
       "  minimum time:     143.481 μs (0.00% GC)\n",
       "  median time:      233.346 μs (0.00% GC)\n",
       "  mean time:        278.571 μs (7.13% GC)\n",
       "  maximum time:     8.286 ms (94.75% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LSODA\n",
    "@benchmark solve(prob1,lsoda()) # Default method of SciPy, deSolve, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Generic Algorithms to Propogate Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
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   "outputs": [
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     "execution_count": 42,
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   "source": [
    "using Measurements\n",
    "u0 = [1.0 ± 0.0 ,1.0 ± 0.0]\n",
    "p = (1.5 ± 0.0,1.0 ± 0.1,3.0 ± 0.2,1.0 ± 0.1)\n",
    "prob_error = ODEProblem(f,u0,tspan,p)\n",
    "sol = solve(prob_error,Tsit5(), saveat=0.2)\n",
    "plot(sol)"
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   "source": [
    "## Generic Algorithms to Calculate Sensitivities"
   ]
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  {
   "cell_type": "code",
   "execution_count": 54,
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:middle;\" transform=\"rotate(0, 236.834, 1494.48)\" x=\"236.834\" y=\"1494.48\">0.0</text>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:end;\" transform=\"rotate(0, 152.123, 1029.62)\" x=\"152.123\" y=\"1029.62\">-20</text>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:end;\" transform=\"rotate(0, 152.123, 382.941)\" x=\"152.123\" y=\"382.941\">10</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip0601)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:end;\" transform=\"rotate(0, 152.123, 167.381)\" x=\"152.123\" y=\"167.381\">20</text>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:84; text-anchor:middle;\" transform=\"rotate(0, 1248.69, 73.2)\" x=\"1248.69\" y=\"73.2\">dx/da</text>\n",
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       "<g clip-path=\"url(#clip0601)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66; text-anchor:middle;\" transform=\"rotate(0, 1248.69, 1590.4)\" x=\"1248.69\" y=\"1590.4\">Time</text>\n",
       "</g>\n",
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       "  236.834,581.001 277.309,576.095 317.783,569.329 358.257,559.603 398.731,545.634 439.206,526.07 479.68,500.101 520.154,469.719 560.629,447.345 601.103,478.053 \n",
       "  641.577,654.147 682.051,882.095 722.526,833.359 763,701.099 803.474,630.623 843.949,597.313 884.423,577.759 924.897,561.942 965.371,545.294 1005.85,525.012 \n",
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       "  1451.06,734.984 1491.54,638.658 1532.01,591.407 1572.49,560.828 1612.96,533.924 1653.43,504.524 1693.91,468.641 1734.38,422.975 1774.86,364.816 1815.33,293.489 \n",
       "  1855.81,215.643 1896.28,163.187 1936.75,245.296 1977.23,705.22 2017.7,1403.28 2058.18,1362.12 2098.65,957.842 2139.13,731.532 2179.6,629.253 2220.07,574.218 \n",
       "  2260.55,534.129 \n",
       "  \"/>\n",
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       "1958.43,330.464 2249.26,330.464 2249.26,209.504 1958.43,209.504 \n",
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       "  1982.43,269.984 2126.43,269.984 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip0601)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:start;\" transform=\"rotate(0, 2150.43, 287.484)\" x=\"2150.43\" y=\"287.484\">y1</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using ForwardDiff: Dual\n",
    "p1dual = Dual{Float64}(1.5, (1.0, 0.0))\n",
    "p2dual = Dual{Float64}(1.0, (0.0, 1.0))\n",
    "pdual = (p1dual, p2dual, 3.0, 1.0)\n",
    "u0 = [Dual{Float64}(1.0, (0.0, 0.0)),Dual{Float64}(1.0, (0.0, 0.0))]\n",
    "prob_dual = ODEProblem(f,u0,tspan,pdual)\n",
    "sol_dual = solve(prob_dual,Tsit5(), saveat=0.2)\n",
    "\n",
    "timepoints = [i for i in sol_dual.t]\n",
    "sensitivity_forward_diff = [i[1].partials.values[1] for i in sol_dual.u]\n",
    "Plots.plot(timepoints,sensitivity_forward_diff,title=\"dx/da\",lw=3,xaxis=\"Time\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Generic Algorithms for Arbitrary Precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{BigFloat,1}:\n",
       " 1.010967945441596789719381858565413753168637694636043181123471126802488483367416    \n",
       " 9.590701157969237149065086474592525107928794966861429243883755987604756818548128e-01"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = big.((1.5,1.0,3.0,1.0)); u0 = big.([1.0,1.0])\n",
    "tspan = big.((0.0,10.0))\n",
    "prob1 = ODEProblem(f,u0,tspan,p)\n",
    "sol = solve(prob1,Vern9(),abstol=1e-25,reltol=1e-25)\n",
    "sol[10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Generic Algorithms for Units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "ename": "Unitful.DimensionError",
     "evalue": "DimensionError: 1.5 kg s^-1 and 1.0 kg^2 s^-1 are not dimensionally compatible.",
     "output_type": "error",
     "traceback": [
      "DimensionError: 1.5 kg s^-1 and 1.0 kg^2 s^-1 are not dimensionally compatible.",
      "",
      "Stacktrace:",
      " [1] -(::Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}}, ::Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(2//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 2//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(2//1), Unitful.Dimension{:Time}(-1//1))}}}) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\Unitful\\src\\quantities.jl:85",
      " [2] f(::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1}, ::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1}, ::NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}}, ::Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}) at .\\In[32]:5",
      " [3] (::ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing})(::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1}, ::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1}, ::Vararg{Any,N} where N) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\DiffEqBase\\src\\diffeqfunction.jl:106",
      " [4] initialize!(::OrdinaryDiffEq.ODEIntegrator{Tsit5,Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}},Float64,Float64,Array{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1},1},ODESolution{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},2,Array{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},1},Nothing,Nothing,Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1},Array{Array{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1},1},1},ODEProblem{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Tuple{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}},true,NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem},Tsit5,OrdinaryDiffEq.InterpolationData{ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1},Array{Array{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1},1},1},OrdinaryDiffEq.Tsit5Cache{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.Tsit5Cache{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.DEOptions{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Float64,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),CallbackSet{Tuple{},Tuple{}},typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN),typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE),typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK),DataStructures.BinaryHeap{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},DataStructures.LessThan},DataStructures.BinaryHeap{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},DataStructures.LessThan},Nothing,Nothing,Int64,Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1}},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1}}, ::OrdinaryDiffEq.Tsit5Cache{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1), Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1)),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1), Unitful.Dimension{:Time}(-1//1))}}},1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}}) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\OrdinaryDiffEq\\src\\perform_step\\low_order_rk_perform_step.jl:580",
      " [5] #__init#203(::Int64, ::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1}, ::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1}, ::Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},1}, ::Nothing, ::Bool, ::Nothing, ::Bool, ::Bool, ::Nothing, ::Bool, ::Bool, ::Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}, ::Bool, ::Rational{Int64}, ::Nothing, ::Nothing, ::Int64, ::Rational{Int64}, ::Int64, ::Int64, ::Rational{Int64}, ::Bool, ::Int64, ::Nothing, ::Nothing, ::Int64, ::Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}, ::Float64, ::typeof(DiffEqBase.ODE_DEFAULT_NORM), ::typeof(LinearAlgebra.opnorm), ::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), ::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Bool, ::Int64, ::String, ::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), ::Nothing, ::Bool, ::Bool, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::typeof(DiffEqBase.__init), ::ODEProblem{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Tuple{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}},true,NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::Tsit5, ::Array{Any,1}, ::Array{Any,1}, ::Array{Any,1}, ::Type{Val{true}}) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\OrdinaryDiffEq\\src\\solve.jl:260",
      " [6] __init(::ODEProblem{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Tuple{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}},true,NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::Tsit5, ::Array{Any,1}, ::Array{Any,1}, ::Array{Any,1}, ::Type{Val{true}}) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\OrdinaryDiffEq\\src\\solve.jl:61",
      " [7] #__solve#202(::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::ODEProblem{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Tuple{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}},true,NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::Tsit5, ::Array{Any,1}, ::Array{Any,1}, ::Array{Any,1}, ::Type{Val{true}}) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\OrdinaryDiffEq\\src\\solve.jl:6",
      " [8] __solve at C:\\Users\\Chris Rackauckas\\.julia\\dev\\OrdinaryDiffEq\\src\\solve.jl:6 [inlined] (repeats 3 times)",
      " [9] #solve#429(::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::ODEProblem{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Tuple{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}},true,NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::Tsit5) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\DiffEqBase\\src\\solve.jl:37",
      " [10] solve(::ODEProblem{Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1},Tuple{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}},Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}},true,NTuple{4,Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0, -1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(-1//1),)}}}},ODEFunction{true,typeof(f),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Nothing,DiffEqBase.StandardODEProblem}, ::Tsit5) at C:\\Users\\Chris Rackauckas\\.julia\\dev\\DiffEqBase\\src\\solve.jl:25",
      " [11] top-level scope at In[62]:5"
     ]
    }
   ],
   "source": [
    "using Unitful\n",
    "p = (1.5,1.0,3.0,1.0)./u\"s\"; u0 = [1.0u\"kg\",1.0u\"kg\"]\n",
    "tspan = (0.0u\"s\",10.0u\"s\")\n",
    "prob_units = ODEProblem(f,u0,tspan,p)\n",
    "sol = solve(prob_units,Tsit5())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.2640893954264825 s, Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}}[4.39301 kg, 4.19467 kg])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#= \n",
    "f = @ode_def LotkaVolterra begin\n",
    "  d🐁  = α*🐁 - β*🐁*🐈\n",
    "  d🐈 = -γ*🐈 + δ*🐁*🐈\n",
    "end α β γ δ\n",
    "=#\n",
    "p = (1.5,1.0/u\"kg\",3.0,1.0/u\"kg\")./u\"s\"; u0 = [1.0u\"kg\",1.0u\"kg\"]\n",
    "tspan = (0.0u\"s\",10.0u\"s\")\n",
    "prob_units = ODEProblem(f,u0,tspan,p)\n",
    "sol = solve(prob_units,Tsit5())\n",
    "sol.t[10],sol[10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Other Features of DifferentialEquations.jl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The solution is a continuous function by default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Gram,Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}(3, 1//1),),Unitful.Dimensions{(Unitful.Dimension{:Mass}(1//1),)}}},1}:\n",
       " 5.338696330932268 kg\n",
       " 3.608369936346481 kg"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol(5.5u\"s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Easily Change to Stochastic Differential Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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       "  1449.91,799.474 1451.72,806.421 1453.5,833.033 1455.26,838.567 1457.04,845.835 1458.8,860.465 1460.56,860.744 1462.35,853.593 1464.14,854.592 1465.9,863.21 \n",
       "  1467.65,881.119 1469.37,878.874 1471.11,879.737 1472.82,891.232 1474.52,908.479 1476.19,900.878 1477.86,930.85 1479.46,932.826 1481.07,945.435 1482.63,967.859 \n",
       "  1484.18,984.952 1485.74,994.114 1487.33,1010.92 1488.91,1022.01 1490.5,1028.48 1492.09,1027.73 1493.7,1043.44 1495.31,1051.04 1496.97,1058.38 1498.63,1072.22 \n",
       "  1500.31,1077.75 1502.04,1069.07 1503.81,1072.94 1505.59,1076.53 1507.43,1078.05 1509.32,1082.5 1511.21,1097.7 1513.13,1105.12 1515.06,1112.23 1517.01,1124.45 \n",
       "  1518.96,1121.28 1520.91,1130.89 1522.88,1130.85 1524.84,1132.13 1526.77,1133.97 1528.7,1145.22 1530.66,1147.4 1532.6,1152.56 1534.56,1154.72 1536.51,1156.8 \n",
       "  1538.43,1154.16 1540.37,1163.27 1542.33,1157.38 1544.28,1160.77 1546.26,1165.3 1548.24,1157.74 1550.26,1168.4 1552.26,1172.89 1554.27,1177.94 1556.31,1172.36 \n",
       "  1558.4,1168.87 1560.45,1173.98 1562.57,1175.45 1564.69,1172.49 1566.85,1174.64 1569.04,1170.56 1571.24,1169.82 1573.45,1169.13 1575.68,1163.4 1577.94,1174.48 \n",
       "  1580.23,1171.61 1582.53,1173.8 1584.81,1184.26 1587.09,1193.35 1589.35,1194.5 1591.61,1202.88 1593.91,1206.93 1596.18,1205.88 1598.45,1212.99 1600.68,1212.88 \n",
       "  1602.93,1215.68 1605.18,1216.21 1607.45,1216.45 1609.74,1207.81 1612.05,1211.83 1614.37,1212.24 1616.74,1216.39 1619.14,1224.66 1621.5,1227.66 1623.87,1226.18 \n",
       "  1626.24,1228.76 1628.7,1232.56 1631.06,1237.58 1633.46,1238.07 1635.83,1241.92 1638.24,1237.39 1640.66,1239.6 1643.05,1241.28 1645.46,1239.15 1647.9,1243.76 \n",
       "  1650.35,1240.56 1652.83,1244.83 1655.32,1243.22 1657.8,1240.79 1660.32,1239.26 1662.88,1240.33 1665.42,1236.28 1668.02,1240.56 1670.64,1244.77 1673.31,1240.51 \n",
       "  1675.94,1239.18 1678.6,1236.82 1681.27,1230.86 1683.98,1229.9 1686.75,1225.45 1689.5,1232.07 1692.29,1222.2 1695.13,1209.28 1697.99,1200.08 1700.95,1199.75 \n",
       "  1703.91,1209.02 1706.89,1217.08 1709.94,1222.38 1712.97,1222.57 1716.02,1211.53 1719.09,1211.66 1722.18,1215.41 1725.28,1210.95 1728.47,1218.23 1731.53,1222.91 \n",
       "  1734.64,1219.61 1737.78,1216.9 1740.81,1225.44 1743.94,1220.96 1747.08,1221.73 1750.21,1217.42 1753.35,1221.88 1756.49,1217.35 1759.68,1212.78 1762.85,1207.01 \n",
       "  1766.07,1195.48 1769.35,1186.32 1772.66,1185.41 1775.98,1170.59 1779.38,1171.9 1782.74,1159.29 1786.2,1158.82 1789.61,1160.31 1793.02,1144.42 1796.51,1146.68 \n",
       "  1799.96,1130.34 1803.48,1107.83 1807.06,1108.01 1810.53,1099.91 1814.1,1087.48 1817.68,1067.24 1821.34,1046.82 1824.99,1035.28 1828.63,1028.25 1832.24,1021.49 \n",
       "  1835.85,1018.82 1839.41,1017.05 1843.01,1010.73 1846.59,998.301 1850.2,988.962 1853.77,979.523 1857.36,980.21 1860.87,987.365 1864.41,970.919 1868.02,960.224 \n",
       "  1871.55,959.851 1875.06,949.117 1878.64,915.033 1882.28,921.951 1885.72,896.689 1889.32,894.488 1892.74,896.575 1896.18,889.259 1899.59,901.294 1902.94,913.124 \n",
       "  1906.28,893.063 1909.69,874.745 1913.05,866.077 1916.38,844.009 1919.7,837.205 1922.94,834.431 1926.17,824.668 1929.4,804.089 1932.61,768.167 1935.84,722.052 \n",
       "  1939.07,711.814 1942.16,693.999 1945.27,677.654 1948.33,649.321 1951.4,605.733 1954.45,569.45 1957.42,558.978 1960.29,537.037 1963.14,544.137 1965.92,528.071 \n",
       "  1968.7,536.605 1971.43,502.334 1974.18,490.747 1976.85,509.923 1979.51,499.195 1982.15,492.951 1984.78,494.987 1987.35,495.77 1989.95,497.766 1992.52,490.119 \n",
       "  1995.11,504.513 1997.67,503.277 2000.23,464.412 2002.78,454.301 2005.24,436.426 2007.67,400.992 2010.07,403.383 2012.36,403.612 2014.66,342.244 2016.92,280.731 \n",
       "  2019.06,285.855 2021.12,278.799 2023.12,269.371 2025.06,246.095 2026.92,223.159 2028.74,205.848 2030.51,239.797 2032.19,229.421 2033.85,197.882 2035.48,186.036 \n",
       "  2037.08,152.372 2038.59,151.192 2040.09,156.559 2041.55,166.745 2042.98,135.248 2044.38,157.641 2045.75,200.975 2047.1,197.028 2048.48,160.425 2049.84,163.558 \n",
       "  2051.16,169.053 2052.47,201.652 2053.78,151.595 2055.08,148.003 2056.34,139.803 2057.57,146.826 2058.8,129.984 2060.04,124.41 2061.23,115.971 2062.4,124.878 \n",
       "  2063.57,143.322 2064.73,141.005 2065.9,165.753 2067.04,179.73 2068.2,194.537 2069.36,175.742 2070.51,164.933 2071.65,193.487 2072.79,201.734 2073.94,220.015 \n",
       "  2075.12,217.75 2076.27,197.6 2077.42,192.619 2078.56,199.023 2079.69,219.578 2080.83,203.391 2081.95,193.952 2083.07,163.834 2084.15,146.94 2085.22,160.232 \n",
       "  2086.28,143.08 2087.33,135.293 2088.36,112.335 2089.38,118.947 2090.36,106.982 2091.34,105.678 2092.3,115.322 2093.25,113.746 2094.19,92.6172 2095.13,103.46 \n",
       "  2096.05,104.802 2096.95,87.1122 2097.86,86.6754 2098.74,104.988 2099.62,111.726 2100.5,115.559 2101.37,118.038 2102.23,123.889 2103.08,115.267 2103.94,97.6568 \n",
       "  2104.78,121.642 2105.61,122.122 2106.43,159.906 2107.26,162.712 2108.08,157.367 2108.91,171.497 2109.72,179.036 2110.53,216.211 2111.33,233.216 2112.15,241.115 \n",
       "  2112.96,270.029 2113.77,265.122 2114.6,301.255 2115.42,275.255 2116.28,291.511 2117.1,311.381 2117.93,319.453 2118.76,348.412 2119.6,366.035 2120.45,382.445 \n",
       "  2121.3,398.002 2122.15,412.011 2123.01,419.347 2123.87,403.659 2124.76,413.473 2125.63,438.074 2126.5,445.132 2127.37,470.703 2128.25,471.438 2129.14,464.855 \n",
       "  2130.03,483.436 2130.93,481.031 2131.84,472.513 2132.75,484.258 2133.65,500.657 2134.56,506.394 2135.49,528.368 2136.41,539.223 2137.35,549.64 2138.28,550.818 \n",
       "  2139.21,579.513 2140.14,591.78 2141.09,604.288 2142.03,603.058 2142.99,597.059 2143.95,610.489 2144.92,631.894 2145.89,645.212 2146.88,667.384 2147.86,682.754 \n",
       "  2148.86,695.47 2149.87,712.988 2150.88,734.089 2151.91,756.991 2152.96,768.729 2154.03,786.729 2155.11,786.872 2156.2,801.35 2157.29,803.1 2158.39,818.058 \n",
       "  2159.49,819.318 2160.59,821.618 2161.7,827.695 2162.81,833.826 2163.93,855.284 2165.04,858.236 2166.17,870.127 2167.28,877.735 2168.4,891.445 2169.51,880.497 \n",
       "  2170.66,895.333 2171.78,904.498 2172.91,918.623 2174.04,924.192 2175.16,935.509 2176.29,937.446 2177.44,941.898 2178.59,951.156 2179.74,973.248 2180.9,981.282 \n",
       "  2182.09,983.811 2183.29,986.427 2184.49,997.387 2185.7,1003.76 2186.92,998.892 2188.17,998.11 2189.43,1003.94 2190.69,1006.47 2191.96,1028.67 2193.23,1039.25 \n",
       "  2194.53,1049.74 2195.84,1051.59 2197.14,1059.53 2198.44,1065.17 2199.74,1071.67 2201.04,1077.05 2202.37,1088.18 2203.71,1097.63 2205.07,1099.74 2206.45,1111.74 \n",
       "  2207.83,1119.89 2209.23,1128.35 2210.65,1132.49 2212.1,1135.2 2213.56,1145.73 2215.02,1152.96 2216.48,1152.2 2217.97,1152.12 2219.44,1165.21 2220.9,1162.62 \n",
       "  2222.4,1170.27 2223.89,1168.49 2225.4,1164.56 2226.91,1163.24 2228.44,1164.4 2229.98,1171.04 2231.54,1177.09 2233.1,1187.43 2234.67,1192.64 2236.23,1194.87 \n",
       "  2237.81,1202.43 2239.39,1203.5 2240.97,1207.3 2242.57,1208.76 2244.15,1212.67 2245.74,1215.45 2247.34,1220.99 2248.98,1224.84 2250.63,1224.48 2252.31,1226.05 \n",
       "  2253.97,1226.59 2255.64,1228.42 2257.34,1237.57 2259.02,1244.47 2260.7,1245.17 2262.38,1245.04 2264.06,1248.42 2265.77,1246.17 2267.5,1249.69 2269.24,1249.18 \n",
       "  2270.98,1249.08 2272.72,1252.48 2274.52,1255.18 2276.29,1252.1 2278.08,1257.44 2279.89,1257.83 2281.73,1258.95 2283.58,1258 2285.43,1261.2 2287.31,1261.5 \n",
       "  2289.22,1263.63 2291.1,1266.01 2293,1263.56 2294.93,1258.86 2296.88,1259.56 2298.85,1264.14 2300.86,1266.44 2302.88,1266.89 2304.88,1270.5 2306.91,1270.78 \n",
       "  2308.94,1270.34 2311.01,1271.36 2313.09,1278.03 2315.21,1276.16 2317.29,1275.11 2319.42,1281.06 2321.26,1285.98 \n",
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       "  122.456,1251.47 122.648,1250.8 122.864,1253.14 123.108,1252.62 123.381,1253.28 123.689,1253.81 124.035,1253.99 124.425,1255.29 124.863,1258.62 125.356,1258.94 \n",
       "  125.911,1262.3 126.534,1260.9 127.236,1260.67 128.026,1261.18 128.914,1259.78 129.914,1260.49 131.038,1261.13 132.303,1265.21 133.726,1262.77 135.327,1267.74 \n",
       "  137.053,1270.81 138.934,1274.74 140.949,1280.75 143.073,1283.96 145.335,1283.08 147.727,1291.15 150.18,1292.04 152.773,1297.13 155.423,1304.94 158.143,1304.37 \n",
       "  160.98,1307.51 163.843,1311.86 166.792,1312.96 169.778,1315.75 172.809,1320.23 175.873,1317.89 179.02,1320.99 182.147,1322.73 185.347,1325.39 188.559,1329.13 \n",
       "  191.801,1332.34 195.062,1334.9 198.39,1336.39 201.697,1342.74 205.021,1346.14 208.366,1347.36 211.74,1349.43 215.168,1349.77 218.629,1350.39 222.065,1352.95 \n",
       "  225.52,1357.17 228.983,1358.58 232.502,1360.31 236.047,1362.99 239.54,1362.62 243.071,1362.89 246.612,1362.47 250.111,1363.15 253.611,1364.9 257.113,1366.03 \n",
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       "  294.368,1379.39 297.647,1380.36 300.852,1380.32 304.142,1381.32 307.327,1384 310.533,1383.4 313.698,1385.37 316.821,1384.28 319.97,1384.84 323.152,1385.47 \n",
       "  326.25,1385.23 329.338,1384.18 332.398,1384.37 335.519,1386.95 338.558,1388.64 341.585,1388.11 344.602,1388.96 347.626,1387.82 350.582,1387.05 353.547,1385.9 \n",
       "  356.529,1384.53 359.528,1384.14 362.474,1386.26 365.489,1386.07 368.491,1384.55 371.462,1383.33 374.415,1382.16 377.325,1383.2 380.213,1384.56 383.104,1380.92 \n",
       "  385.961,1381.48 388.833,1379.58 391.817,1379 394.771,1379.14 397.725,1378.15 400.583,1377.24 403.446,1375.05 406.322,1374.47 409.166,1373.45 412.07,1376.58 \n",
       "  414.935,1377.46 417.77,1377.47 420.602,1376.63 423.483,1377.93 426.359,1377.58 429.193,1374.42 431.984,1372.8 434.806,1372.69 437.603,1373.45 440.43,1371.81 \n",
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       "  545.671,1266.57 547.883,1261.95 550.007,1259.74 552.057,1254.43 554.08,1248.57 556.029,1249.66 557.897,1242.85 559.759,1236.39 561.569,1230.21 563.365,1221.53 \n",
       "  565.095,1212.21 566.766,1204.9 568.363,1194.33 569.928,1188.9 571.394,1180.26 572.798,1171.34 574.168,1160.34 575.512,1159.82 576.789,1153.15 578.056,1146.32 \n",
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       "  591.078,1094.58 592.24,1090.23 593.391,1083.5 594.533,1067.92 595.662,1058.42 596.764,1052.74 597.84,1042.15 598.896,1036.35 599.942,1025.81 601,1009.73 \n",
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       "  613.037,923.849 614.137,918.975 615.218,903.786 616.317,890.688 617.413,876.553 618.5,866.966 619.581,832.559 620.656,835.182 621.688,830.121 622.737,819.51 \n",
       "  623.789,807.427 624.834,799.483 625.876,786.993 626.919,786.635 627.959,774.818 629.022,768.317 630.075,760.816 631.158,764.556 632.239,760.907 633.337,751.574 \n",
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       "  845.831,1222.5 848.125,1212.05 850.511,1216.9 852.813,1221.99 855.164,1226.47 857.541,1227.48 859.943,1228.02 862.369,1231.25 864.822,1233.51 867.302,1244.44 \n",
       "  869.771,1251.29 872.278,1258.1 874.778,1262.92 877.318,1269.17 879.894,1273.15 882.51,1273.16 885.177,1281.83 887.822,1284.37 890.535,1287.32 893.271,1297 \n",
       "  895.988,1302.45 898.784,1303.26 901.641,1300.85 904.561,1303.52 907.48,1306.97 910.43,1310.69 913.446,1310.88 916.495,1312.89 919.575,1312.37 922.691,1314.1 \n",
       "  925.819,1318.85 928.933,1325.81 932.073,1329.84 935.275,1337.24 938.468,1338.25 941.74,1338.38 945.035,1346.52 948.323,1345.6 951.73,1347.2 955.078,1349.32 \n",
       "  958.448,1351.29 961.829,1354.37 965.236,1356.29 968.634,1357.67 972.071,1361.55 975.545,1363.58 978.994,1367.47 982.428,1368.11 985.868,1369.96 989.306,1371.8 \n",
       "  992.737,1374.04 996.197,1376.54 999.687,1377.2 1003.1,1378.66 1006.51,1378.94 1009.97,1378.84 1013.44,1380.45 1016.86,1378 1020.31,1378.32 1023.74,1379.44 \n",
       "  1027.19,1379.31 1030.62,1380.13 1033.97,1384.19 1037.37,1385.87 1040.74,1387.7 1044.18,1389.26 1047.57,1391.06 1050.94,1391.24 1054.22,1390 1057.53,1391.79 \n",
       "  1060.75,1391.59 1063.98,1391.68 1067.23,1392.98 1070.4,1394.42 1073.55,1395.32 1076.75,1395.55 1079.86,1394.58 1083.02,1393.98 1086.11,1394.56 1089.22,1395.22 \n",
       "  1092.35,1395.95 1095.42,1396.85 1098.42,1397.63 1101.43,1398.55 1104.4,1399.52 1107.33,1398.74 1110.25,1399.15 1113.14,1398.49 1116.02,1399.74 1118.87,1400.1 \n",
       "  1121.74,1399.65 1124.64,1399.44 1127.44,1400.32 1130.26,1401.05 1133.11,1400.32 1135.9,1399.4 1138.73,1399.75 1141.59,1400.19 1144.46,1399.85 1147.24,1399.44 \n",
       "  1150.09,1398.76 1152.86,1398.27 1155.62,1399.18 1158.34,1398.33 1161.07,1399.22 1163.8,1398.86 1166.48,1398.69 1169.19,1397.53 1171.87,1395.58 1174.62,1394.8 \n",
       "  1177.3,1394.46 1179.96,1393.67 1182.63,1392.14 1185.31,1390.9 1188,1391.69 1190.74,1392.56 1193.37,1392.83 1196.03,1392.56 1198.71,1391.91 1201.34,1389.65 \n",
       "  1203.98,1388.54 1206.62,1388.52 1209.28,1388.06 1211.92,1387.13 1214.59,1385 1217.22,1383.93 1219.85,1382.68 1222.51,1380.97 1225.15,1381.15 1227.84,1380.06 \n",
       "  1230.48,1377.15 1233.17,1375.97 1235.85,1376.5 1238.53,1376.34 1241.25,1374.44 1243.9,1372.17 1246.64,1371.28 1249.29,1369.44 1252.01,1369.61 1254.72,1367.81 \n",
       "  1257.37,1367.05 1260.02,1365.58 1262.67,1363.43 1265.34,1359.56 1267.93,1357.05 1270.51,1352.84 1273.11,1351.39 1275.66,1346.42 1278.22,1341.85 1280.77,1340.55 \n",
       "  1283.29,1338.43 1285.81,1334.73 1288.29,1333.66 1290.72,1332.42 1293.18,1331.59 1295.55,1325.26 1297.94,1322.79 1300.29,1318.68 1302.64,1317.33 1304.95,1316.05 \n",
       "  1307.19,1313.05 1309.37,1309 1311.51,1303.73 1313.58,1300.74 1315.61,1296.72 1317.63,1292.09 1319.62,1285.49 1321.56,1275.77 1323.48,1268.26 1325.32,1264.24 \n",
       "  1327.13,1260.33 1328.92,1256.77 1330.72,1253.54 1332.5,1249.21 1334.25,1244.23 1335.98,1237.38 1337.73,1230.15 1339.49,1218.36 1341.28,1214.93 1343.02,1213.1 \n",
       "  1344.82,1207.18 1346.67,1203.3 1348.5,1195.77 1350.34,1184.07 1352.22,1181.37 1354.06,1170.38 1355.95,1164.88 1357.77,1152 1359.59,1140.11 1361.37,1131.82 \n",
       "  1363.12,1126.45 1364.84,1102.66 1366.61,1093.89 1368.31,1091.48 1370.02,1085.41 1371.75,1067.5 1373.54,1054.05 1375.33,1055.66 1377.05,1045.74 1378.8,1043.56 \n",
       "  1380.54,1038.49 1382.33,1021.75 1384.15,1015.6 1385.94,1003.61 1387.76,1001.36 1389.55,990.782 1391.35,976.944 1393.17,960.498 1395,964.351 1396.78,971.783 \n",
       "  1398.58,962.74 1400.4,950.611 1402.19,944.351 1403.97,934.525 1405.72,912.986 1407.51,895.461 1409.23,887.33 1410.94,861.56 1412.65,834.018 1414.32,839.195 \n",
       "  1415.95,842.069 1417.57,833.377 1419.2,833.984 1420.79,828.865 1422.4,831.55 1424.01,826.794 1425.64,825.525 1427.3,806.709 1428.95,812.04 1430.59,811.398 \n",
       "  1432.26,827.193 1433.92,838.964 1435.61,827.868 1437.36,836.004 1439.1,820.824 1440.9,810.342 1442.68,808.958 1444.48,807.723 1446.28,789.437 1448.1,789.351 \n",
       "  1449.91,781.796 1451.72,776.482 1453.5,764.611 1455.26,760.584 1457.04,756.672 1458.8,780.13 1460.56,776.649 1462.35,753.255 1464.14,756.068 1465.9,745.033 \n",
       "  1467.65,748.596 1469.37,736.716 1471.11,741.195 1472.82,720.897 1474.52,716.449 1476.19,699.69 1477.86,688.651 1479.46,674.867 1481.07,670.68 1482.63,685.192 \n",
       "  1484.18,714.615 1485.74,715.186 1487.33,709.427 1488.91,716.179 1490.5,723.3 1492.09,733.077 1493.7,751.711 1495.31,755.697 1496.97,770.69 1498.63,791.573 \n",
       "  1500.31,800.951 1502.04,810.227 1503.81,832.955 1505.59,844.742 1507.43,844.826 1509.32,853.35 1511.21,855.45 1513.13,863.185 1515.06,863.942 1517.01,856.028 \n",
       "  1518.96,864.723 1520.91,857.085 1522.88,842.941 1524.84,844.67 1526.77,869.254 1528.7,868.544 1530.66,873.692 1532.6,871.476 1534.56,864.404 1536.51,871.237 \n",
       "  1538.43,887.253 1540.37,881.887 1542.33,895.46 1544.28,908.519 1546.26,914.24 1548.24,912.386 1550.26,925.186 1552.26,946.518 1554.27,956.863 1556.31,945.625 \n",
       "  1558.4,964.946 1560.45,979.416 1562.57,983.841 1564.69,992.358 1566.85,989.453 1569.04,985.075 1571.24,990.183 1573.45,1000.85 1575.68,1006.83 1577.94,1006.46 \n",
       "  1580.23,998.388 1582.53,1003.3 1584.81,1012.49 1587.09,1020.06 1589.35,1037.69 1591.61,1036.61 1593.91,1032.47 1596.18,1030.34 1598.45,1049.1 1600.68,1062.76 \n",
       "  1602.93,1075.73 1605.18,1085.4 1607.45,1089.37 1609.74,1099.04 1612.05,1115.55 1614.37,1120.11 1616.74,1115.48 1619.14,1119.65 1621.5,1124.5 1623.87,1136.44 \n",
       "  1626.24,1125.58 1628.7,1136.57 1631.06,1142.46 1633.46,1151.4 1635.83,1157.21 1638.24,1156.14 1640.66,1168.76 1643.05,1181.67 1645.46,1185.64 1647.9,1194.8 \n",
       "  1650.35,1197.69 1652.83,1199.37 1655.32,1205.17 1657.8,1212.94 1660.32,1216.38 1662.88,1223.31 1665.42,1231.04 1668.02,1231.8 1670.64,1225.79 1673.31,1231.99 \n",
       "  1675.94,1240.08 1678.6,1246.62 1681.27,1249.52 1683.98,1251.61 1686.75,1255.53 1689.5,1261.17 1692.29,1261.77 1695.13,1268.55 1697.99,1267.72 1700.95,1273.43 \n",
       "  1703.91,1280.77 1706.89,1278.24 1709.94,1279.59 1712.97,1280.4 1716.02,1279.83 1719.09,1280.46 1722.18,1279.96 1725.28,1272.45 1728.47,1280.74 1731.53,1283.07 \n",
       "  1734.64,1280.69 1737.78,1292.56 1740.81,1297.34 1743.94,1297.81 1747.08,1296.07 1750.21,1301.69 1753.35,1307.34 1756.49,1306.51 1759.68,1313.38 1762.85,1318.93 \n",
       "  1766.07,1322.03 1769.35,1325.11 1772.66,1327.98 1775.98,1329.92 1779.38,1333.81 1782.74,1335.57 1786.2,1338.57 1789.61,1343.96 1793.02,1347.1 1796.51,1347.98 \n",
       "  1799.96,1352.31 1803.48,1353.66 1807.06,1351.72 1810.53,1347.8 1814.1,1346.77 1817.68,1345.11 1821.34,1346.53 1824.99,1349.11 1828.63,1349.38 1832.24,1351.3 \n",
       "  1835.85,1351.15 1839.41,1352.05 1843.01,1352.33 1846.59,1353.53 1850.2,1354.39 1853.77,1353.19 1857.36,1353.09 1860.87,1352.18 1864.41,1352.76 1868.02,1354.79 \n",
       "  1871.55,1354.4 1875.06,1353.18 1878.64,1355.73 1882.28,1355.79 1885.72,1358.47 1889.32,1357.79 1892.74,1360.35 1896.18,1360.06 1899.59,1361.96 1902.94,1361.94 \n",
       "  1906.28,1361.31 1909.69,1363.65 1913.05,1365.31 1916.38,1367.29 1919.7,1366.77 1922.94,1366.17 1926.17,1367.08 1929.4,1368.17 1932.61,1366.69 1935.84,1365.51 \n",
       "  1939.07,1363.54 1942.16,1363.88 1945.27,1360.38 1948.33,1360.34 1951.4,1359.16 1954.45,1357.01 1957.42,1355.71 1960.29,1354.88 1963.14,1352.45 1965.92,1353.12 \n",
       "  1968.7,1349.5 1971.43,1346.43 1974.18,1343.03 1976.85,1336.1 1979.51,1333.7 1982.15,1328.58 1984.78,1329.47 1987.35,1324.23 1989.95,1319.56 1992.52,1311.99 \n",
       "  1995.11,1305.38 1997.67,1304.97 2000.23,1304.89 2002.78,1304.08 2005.24,1306.04 2007.67,1302.46 2010.07,1301.64 2012.36,1300.71 2014.66,1295.86 2016.92,1290.12 \n",
       "  2019.06,1281.21 2021.12,1277.08 2023.12,1271.15 2025.06,1269.61 2026.92,1263.15 2028.74,1251.19 2030.51,1249.76 2032.19,1249.53 2033.85,1245.98 2035.48,1238.09 \n",
       "  2037.08,1240.57 2038.59,1232.69 2040.09,1225.96 2041.55,1218.27 2042.98,1214.78 2044.38,1207.84 2045.75,1210.16 2047.1,1207.12 2048.48,1197.83 2049.84,1192.45 \n",
       "  2051.16,1185.17 2052.47,1177.44 2053.78,1173.69 2055.08,1169.93 2056.34,1173.42 2057.57,1171.28 2058.8,1159.1 2060.04,1151.61 2061.23,1151.66 2062.4,1143.33 \n",
       "  2063.57,1139.35 2064.73,1127.74 2065.9,1129.03 2067.04,1124.65 2068.2,1116.4 2069.36,1113.56 2070.51,1111.11 2071.65,1108.46 2072.79,1104.35 2073.94,1086.32 \n",
       "  2075.12,1077.76 2076.27,1074.17 2077.42,1065.73 2078.56,1061.14 2079.69,1050.83 2080.83,1047.26 2081.95,1037.81 2083.07,1039.58 2084.15,1037.39 2085.22,1027.3 \n",
       "  2086.28,1022.81 2087.33,1011.17 2088.36,999.167 2089.38,994.972 2090.36,985.428 2091.34,981.465 2092.3,983.97 2093.25,976.054 2094.19,961.989 2095.13,946.225 \n",
       "  2096.05,948.81 2096.95,933.789 2097.86,923.664 2098.74,913.834 2099.62,900.457 2100.5,885.359 2101.37,877.016 2102.23,872.955 2103.08,857.578 2103.94,842.693 \n",
       "  2104.78,831.657 2105.61,826.327 2106.43,806.504 2107.26,799.632 2108.08,776.945 2108.91,765.473 2109.72,752.819 2110.53,741.821 2111.33,730.168 2112.15,726.411 \n",
       "  2112.96,730.89 2113.77,734.036 2114.6,726.722 2115.42,693.758 2116.28,682.845 2117.1,674.314 2117.93,673.336 2118.76,672.09 2119.6,662.708 2120.45,645.478 \n",
       "  2121.3,624.535 2122.15,636.468 2123.01,651.219 2123.87,639.571 2124.76,617.786 2125.63,603.766 2126.5,608.545 2127.37,610.189 2128.25,614.74 2129.14,613.375 \n",
       "  2130.03,624.489 2130.93,620.27 2131.84,606.38 2132.75,598.717 2133.65,614.402 2134.56,611.498 2135.49,612.498 2136.41,592.943 2137.35,574.57 2138.28,572.699 \n",
       "  2139.21,574.625 2140.14,568.564 2141.09,560.456 2142.03,574.43 2142.99,580.048 2143.95,588.626 2144.92,575.631 2145.89,567.549 2146.88,568.511 2147.86,569.265 \n",
       "  2148.86,562.085 2149.87,577.724 2150.88,579.842 2151.91,585.69 2152.96,596.898 2154.03,587.4 2155.11,566.989 2156.2,559.223 2157.29,563.06 2158.39,550.534 \n",
       "  2159.49,552.597 2160.59,560.677 2161.7,559.767 2162.81,562.266 2163.93,551.952 2165.04,534.638 2166.17,538.217 2167.28,539.855 2168.4,535.786 2169.51,539.354 \n",
       "  2170.66,532.898 2171.78,545.65 2172.91,517.931 2174.04,526.947 2175.16,545.047 2176.29,550.211 2177.44,538.988 2178.59,556.642 2179.74,578.372 2180.9,577.68 \n",
       "  2182.09,577.989 2183.29,567.79 2184.49,574.073 2185.7,595.733 2186.92,597.752 2188.17,609.801 2189.43,606.583 2190.69,609.195 2191.96,627.209 2193.23,624.18 \n",
       "  2194.53,615.572 2195.84,607.754 2197.14,599.116 2198.44,597.24 2199.74,632.18 2201.04,650.322 2202.37,659.924 2203.71,658.215 2205.07,673.073 2206.45,676.01 \n",
       "  2207.83,697.894 2209.23,722.851 2210.65,717.172 2212.1,713.099 2213.56,707.465 2215.02,712.798 2216.48,696.138 2217.97,697.813 2219.44,721.139 2220.9,728.374 \n",
       "  2222.4,731.4 2223.89,728.579 2225.4,743.006 2226.91,752.385 2228.44,769.867 2229.98,771.38 2231.54,771.482 2233.1,770.634 2234.67,782.719 2236.23,787.217 \n",
       "  2237.81,788.327 2239.39,791.622 2240.97,784.609 2242.57,795.652 2244.15,816.246 2245.74,845.122 2247.34,865.187 2248.98,870.131 2250.63,854.865 2252.31,853.374 \n",
       "  2253.97,876.89 2255.64,872.397 2257.34,869.861 2259.02,878.173 2260.7,888.295 2262.38,916.069 2264.06,932.965 2265.77,933.974 2267.5,936.161 2269.24,939.408 \n",
       "  2270.98,965.918 2272.72,962.617 2274.52,972.752 2276.29,995.406 2278.08,1011.73 2279.89,1014.68 2281.73,1017.34 2283.58,1033.65 2285.43,1038.34 2287.31,1036.55 \n",
       "  2289.22,1050.34 2291.1,1066.31 2293,1069.44 2294.93,1079.39 2296.88,1092.25 2298.85,1094.45 2300.86,1094.63 2302.88,1104.54 2304.88,1115.47 2306.91,1129.49 \n",
       "  2308.94,1136.98 2311.01,1142.77 2313.09,1137.01 2315.21,1141.47 2317.29,1141.81 2319.42,1147.26 2321.26,1145 \n",
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       "</svg>\n"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DifferentialEquations\n",
    "function g(du,u,p,t)\n",
    "  du[1] = 0.2u[1]\n",
    "  du[2] = 0.2u[2]\n",
    "end\n",
    "p = (1.5,1.0,3.0,1.0); u0 = [1.0;1.0]\n",
    "tspan = (0.0,10.0)\n",
    "prob1 = SDEProblem(f,g,u0,tspan,p)\n",
    "sol = solve(prob1)\n",
    "using Plots; plot(sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## And Delay Differential Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
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       "  1464.6,818.991 1466.8,817.674 1469,816.344 1471.21,815.003 1473.41,813.648 1475.61,812.281 1477.81,810.9 1480.02,809.506 1482.22,808.098 1484.42,806.676 \n",
       "  1486.62,805.239 1488.82,803.788 1491.03,802.322 1493.23,800.842 1495.43,799.346 1497.63,797.835 1499.83,796.31 1502.04,794.768 1504.24,793.212 1506.44,791.641 \n",
       "  1508.64,790.054 1510.85,788.452 1513.05,786.835 1515.25,785.203 1517.45,783.557 1519.65,781.895 1521.86,780.219 1524.06,778.529 1526.26,776.825 1528.46,775.106 \n",
       "  1530.67,773.374 1532.87,771.629 1535.07,769.871 1537.27,768.101 1539.47,766.318 1541.68,764.523 1543.88,762.717 1546.08,760.899 1548.28,759.072 1550.49,757.234 \n",
       "  1552.69,755.387 1554.89,753.531 1557.09,751.666 1559.29,749.794 1561.5,747.914 1563.7,746.028 1565.9,744.136 1568.1,742.239 1570.31,740.337 1572.51,738.432 \n",
       "  1574.71,736.522 1576.91,734.607 1579.11,732.69 1581.32,730.77 1583.52,728.848 1585.72,726.926 1587.92,725.004 1590.13,723.083 1592.33,721.163 1594.53,719.246 \n",
       "  1596.73,717.332 1598.93,715.422 1601.14,713.516 1603.34,711.616 1605.54,709.721 1607.74,707.834 1609.95,705.953 1612.15,704.081 1614.35,702.217 1616.55,700.363 \n",
       "  1618.75,698.518 1620.96,696.684 1623.16,694.861 1625.36,693.049 1627.56,691.25 1629.77,689.464 1631.97,687.691 1634.17,685.931 1636.37,684.187 1638.57,682.457 \n",
       "  1640.78,680.742 1642.98,679.043 1645.18,677.361 1647.38,675.695 1649.59,674.046 1651.79,672.415 1653.99,670.802 1656.19,669.208 1658.39,667.632 1660.6,666.076 \n",
       "  1662.8,664.539 1665,663.022 1667.2,661.525 1669.41,660.049 1671.61,658.593 1673.81,657.159 1676.01,655.747 1678.21,654.356 1680.42,652.987 1682.62,651.64 \n",
       "  1684.82,650.316 1687.02,649.014 1689.23,647.736 1691.43,646.48 1693.63,645.248 1695.83,644.04 1698.03,642.855 1700.24,641.694 1702.44,640.556 1704.64,639.443 \n",
       "  1706.84,638.354 1709.05,637.29 1711.25,636.25 1713.45,635.236 1715.65,634.246 1717.85,633.282 1720.06,632.343 1722.26,631.43 1724.46,630.542 1726.66,629.681 \n",
       "  1728.86,628.845 1731.07,628.035 1733.27,627.251 1735.47,626.493 1737.67,625.761 1739.88,625.056 1742.08,624.377 1744.28,623.725 1746.48,623.099 1748.68,622.5 \n",
       "  1750.89,621.927 1753.09,621.381 1755.29,620.862 1757.49,620.369 1759.7,619.903 1761.9,619.464 1764.1,619.051 1766.3,618.666 1768.5,618.307 1770.71,617.974 \n",
       "  1772.91,617.669 1775.11,617.39 1777.31,617.137 1779.52,616.911 1781.72,616.712 1783.92,616.539 1786.12,616.393 1788.32,616.273 1790.53,616.179 1792.73,616.111 \n",
       "  1794.93,616.069 1797.13,616.053 1799.34,616.063 1801.54,616.099 1803.74,616.161 1805.94,616.248 1808.14,616.36 1810.35,616.498 1812.55,616.66 1814.75,616.848 \n",
       "  1816.95,617.06 1819.16,617.297 1821.36,617.558 1823.56,617.844 1825.76,618.154 1827.96,618.487 1830.17,618.844 1832.37,619.225 1834.57,619.63 1836.77,620.059 \n",
       "  1838.98,620.511 1841.18,620.986 1843.38,621.485 1845.58,622.006 1847.78,622.551 1849.99,623.117 1852.19,623.706 1854.39,624.318 1856.59,624.951 1858.8,625.605 \n",
       "  1861,626.281 1863.2,626.979 1865.4,627.697 1867.6,628.436 1869.81,629.195 1872.01,629.974 1874.21,630.773 1876.41,631.592 1878.62,632.43 1880.82,633.286 \n",
       "  1883.02,634.162 1885.22,635.055 1887.42,635.967 1889.63,636.896 1891.83,637.843 1894.03,638.806 1896.23,639.787 1898.44,640.783 1900.64,641.795 1902.84,642.823 \n",
       "  1905.04,643.866 1907.24,644.923 1909.45,645.995 1911.65,647.081 1913.85,648.18 1916.05,649.293 1918.26,650.418 1920.46,651.555 1922.66,652.705 1924.86,653.865 \n",
       "  1927.06,655.037 1929.27,656.219 1931.47,657.411 1933.67,658.612 1935.87,659.823 1938.08,661.042 1940.28,662.27 1942.48,663.505 1944.68,664.747 1946.88,665.995 \n",
       "  1949.09,667.25 1951.29,668.51 1953.49,669.775 1955.69,671.045 1957.89,672.318 1960.1,673.595 1962.3,674.875 1964.5,676.157 1966.7,677.44 1968.91,678.726 \n",
       "  1971.11,680.014 1973.31,681.306 1975.51,682.601 1977.71,683.897 1979.92,685.195 1982.12,686.494 1984.32,687.793 1986.52,689.092 1988.73,690.39 1990.93,691.687 \n",
       "  1993.13,692.982 1995.33,694.276 1997.53,695.566 1999.74,696.854 2001.94,698.138 2004.14,699.419 2006.34,700.695 2008.55,701.966 2010.75,703.233 2012.95,704.494 \n",
       "  2015.15,705.749 2017.35,706.999 2019.56,708.242 2021.76,709.478 2023.96,710.708 2026.16,711.93 2028.37,713.144 2030.57,714.351 2032.77,715.55 2034.97,716.74 \n",
       "  2037.17,717.922 2039.38,719.096 2041.58,720.26 2043.78,721.416 2045.98,722.562 2048.19,723.699 2050.39,724.826 2052.59,725.944 2054.79,727.052 2056.99,728.15 \n",
       "  2059.2,729.238 2061.4,730.316 2063.6,731.384 2065.8,732.442 2068.01,733.49 2070.21,734.528 2072.41,735.556 2074.61,736.573 2076.81,737.58 2079.02,738.577 \n",
       "  2081.22,739.564 2083.42,740.541 2085.62,741.509 2087.83,742.466 2090.03,743.413 2092.23,744.351 2094.43,745.279 2096.63,746.198 2098.84,747.108 2101.04,748.008 \n",
       "  2103.24,748.9 2105.44,749.782 2107.65,750.655 2109.85,751.518 2112.05,752.371 2114.25,753.215 2116.45,754.048 2118.66,754.872 2120.86,755.685 2123.06,756.489 \n",
       "  2125.26,757.282 2127.47,758.066 2129.67,758.839 2131.87,759.602 2134.07,760.355 2136.27,761.098 2138.48,761.831 2140.68,762.553 2142.88,763.265 2145.08,763.967 \n",
       "  2147.29,764.658 2149.49,765.34 2151.69,766.011 2153.89,766.671 2156.09,767.322 2158.3,767.962 2160.5,768.592 2162.7,769.211 2164.9,769.821 2167.11,770.42 \n",
       "  2169.31,771.009 2171.51,771.587 2173.71,772.156 2175.91,772.714 2178.12,773.263 2180.32,773.801 2182.52,774.329 2184.72,774.847 2186.92,775.355 2189.13,775.854 \n",
       "  2191.33,776.342 2193.53,776.821 2195.73,777.29 2197.94,777.749 2200.14,778.198 2202.34,778.638 2204.54,779.069 2206.74,779.489 2208.95,779.901 2211.15,780.303 \n",
       "  2213.35,780.696 2215.55,781.08 2217.76,781.455 2219.96,781.821 2222.16,782.178 2224.36,782.526 2226.56,782.865 2228.77,783.196 2230.97,783.518 2233.17,783.832 \n",
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       "  2279.42,788.247 2281.62,788.353 2283.82,788.45 2286.02,788.537 2288.23,788.615 2290.43,788.684 2292.63,788.744 2294.83,788.795 2297.04,788.836 2299.24,788.868 \n",
       "  2301.44,788.891 2303.64,788.905 2305.84,788.91 2308.05,788.906 2310.25,788.892 2312.45,788.87 2314.65,788.84 2316.86,788.8 2319.06,788.752 2321.26,788.695 \n",
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       "  914.047,692.914 916.249,686.952 918.451,681.265 920.653,675.854 922.856,670.722 925.058,665.869 927.26,661.296 929.462,657.003 931.664,652.989 933.867,649.253 \n",
       "  936.069,645.792 938.271,642.604 940.473,639.687 942.675,637.035 944.878,634.645 947.08,632.512 949.282,630.63 951.484,628.992 953.686,627.593 955.889,626.423 \n",
       "  958.091,625.477 960.293,624.743 962.495,624.214 964.698,623.879 966.9,623.728 969.102,623.75 971.304,623.932 973.506,624.262 975.709,624.728 977.911,625.316 \n",
       "  980.113,626.011 982.315,626.799 984.517,627.664 986.72,628.593 988.922,629.615 991.124,630.738 993.326,631.955 995.529,633.261 997.731,634.65 999.933,636.116 \n",
       "  1002.14,637.656 1004.34,639.263 1006.54,640.935 1008.74,642.665 1010.94,644.45 1013.15,646.287 1015.35,648.171 1017.55,650.1 1019.75,652.07 1021.96,654.079 \n",
       "  1024.16,656.124 1026.36,658.202 1028.56,660.312 1030.76,662.451 1032.97,664.618 1035.17,666.811 1037.37,669.03 1039.57,671.273 1041.77,673.54 1043.98,675.83 \n",
       "  1046.18,678.143 1048.38,680.48 1050.58,682.839 1052.79,685.223 1054.99,687.632 1057.19,690.066 1059.39,692.528 1061.59,695.017 1063.8,697.537 1066,700.08 \n",
       "  1068.2,702.647 1070.4,705.239 1072.61,707.856 1074.81,710.501 1077.01,713.175 1079.21,715.879 1081.41,718.614 1083.62,721.382 1085.82,724.182 1088.02,727.017 \n",
       "  1090.22,729.886 1092.43,732.792 1094.63,735.734 1096.83,738.713 1099.03,741.73 1101.23,744.786 1103.44,747.88 1105.64,751.014 1107.84,754.187 1110.04,757.4 \n",
       "  1112.25,760.654 1114.45,763.948 1116.65,767.282 1118.85,770.656 1121.05,774.071 1123.26,777.526 1125.46,781.021 1127.66,784.556 1129.86,788.13 1132.07,791.744 \n",
       "  1134.27,795.396 1136.47,799.086 1138.67,802.814 1140.87,806.578 1143.08,810.379 1145.28,814.216 1147.48,818.087 1149.68,821.992 1151.89,825.929 1154.09,829.898 \n",
       "  1156.29,833.898 1158.49,837.928 1160.69,841.984 1162.9,846.065 1165.1,850.169 1167.3,854.293 1169.5,858.435 1171.71,862.593 1173.91,866.766 1176.11,870.95 \n",
       "  1178.31,875.145 1180.51,879.348 1182.72,883.556 1184.92,887.769 1187.12,891.985 1189.32,896.2 1191.53,900.415 1193.73,904.626 1195.93,908.833 1198.13,913.033 \n",
       "  1200.33,917.225 1202.54,921.407 1204.74,925.577 1206.94,929.735 1209.14,933.878 1211.35,938.005 1213.55,942.114 1215.75,946.205 1217.95,950.275 1220.15,954.324 \n",
       "  1222.36,958.349 1224.56,962.35 1226.76,966.326 1228.96,970.274 1231.17,974.195 1233.37,978.086 1235.57,981.947 1237.77,985.776 1239.97,989.573 1242.18,993.336 \n",
       "  1244.38,997.065 1246.58,1000.76 1248.78,1004.41 1250.99,1008.03 1253.19,1011.62 1255.39,1015.16 1257.59,1018.67 1259.79,1022.14 1262,1025.56 1264.2,1028.95 \n",
       "  1266.4,1032.31 1268.6,1035.62 1270.8,1038.89 1273.01,1042.12 1275.21,1045.31 1277.41,1048.46 1279.61,1051.57 1281.82,1054.64 1284.02,1057.67 1286.22,1060.66 \n",
       "  1288.42,1063.61 1290.62,1066.52 1292.83,1069.38 1295.03,1072.21 1297.23,1075 1299.43,1077.75 1301.64,1080.46 1303.84,1083.13 1306.04,1085.75 1308.24,1088.34 \n",
       "  1310.44,1090.9 1312.65,1093.41 1314.85,1095.88 1317.05,1098.32 1319.25,1100.72 1321.46,1103.09 1323.66,1105.41 1325.86,1107.7 1328.06,1109.96 1330.26,1112.18 \n",
       "  1332.47,1114.37 1334.67,1116.52 1336.87,1118.64 1339.07,1120.73 1341.28,1122.78 1343.48,1124.81 1345.68,1126.8 1347.88,1128.77 1350.08,1130.7 1352.29,1132.6 \n",
       "  1354.49,1134.47 1356.69,1136.32 1358.89,1138.13 1361.1,1139.92 1363.3,1141.68 1365.5,1143.41 1367.7,1145.12 1369.9,1146.8 1372.11,1148.46 1374.31,1150.08 \n",
       "  1376.51,1151.69 1378.71,1153.27 1380.92,1154.82 1383.12,1156.35 1385.32,1157.86 1387.52,1159.35 1389.72,1160.81 1391.93,1162.25 1394.13,1163.67 1396.33,1165.06 \n",
       "  1398.53,1166.44 1400.74,1167.79 1402.94,1169.13 1405.14,1170.44 1407.34,1171.73 1409.54,1173.01 1411.75,1174.26 1413.95,1175.49 1416.15,1176.71 1418.35,1177.91 \n",
       "  1420.56,1179.08 1422.76,1180.24 1424.96,1181.38 1427.16,1182.51 1429.36,1183.61 1431.57,1184.7 1433.77,1185.77 1435.97,1186.82 1438.17,1187.85 1440.38,1188.87 \n",
       "  1442.58,1189.87 1444.78,1190.86 1446.98,1191.83 1449.18,1192.78 1451.39,1193.71 1453.59,1194.63 1455.79,1195.53 1457.99,1196.42 1460.2,1197.29 1462.4,1198.14 \n",
       "  1464.6,1198.98 1466.8,1199.8 1469,1200.6 1471.21,1201.39 1473.41,1202.17 1475.61,1202.92 1477.81,1203.66 1480.02,1204.39 1482.22,1205.1 1484.42,1205.79 \n",
       "  1486.62,1206.46 1488.82,1207.12 1491.03,1207.77 1493.23,1208.4 1495.43,1209.01 1497.63,1209.6 1499.83,1210.18 1502.04,1210.74 1504.24,1211.29 1506.44,1211.82 \n",
       "  1508.64,1212.34 1510.85,1212.83 1513.05,1213.32 1515.25,1213.78 1517.45,1214.23 1519.65,1214.66 1521.86,1215.08 1524.06,1215.48 1526.26,1215.86 1528.46,1216.23 \n",
       "  1530.67,1216.58 1532.87,1216.91 1535.07,1217.23 1537.27,1217.53 1539.47,1217.81 1541.68,1218.08 1543.88,1218.33 1546.08,1218.56 1548.28,1218.78 1550.49,1218.97 \n",
       "  1552.69,1219.16 1554.89,1219.32 1557.09,1219.47 1559.29,1219.6 1561.5,1219.71 1563.7,1219.81 1565.9,1219.89 1568.1,1219.95 1570.31,1219.99 1572.51,1220.02 \n",
       "  1574.71,1220.03 1576.91,1220.02 1579.11,1219.99 1581.32,1219.95 1583.52,1219.88 1585.72,1219.8 1587.92,1219.71 1590.13,1219.59 1592.33,1219.46 1594.53,1219.31 \n",
       "  1596.73,1219.14 1598.93,1218.96 1601.14,1218.75 1603.34,1218.53 1605.54,1218.29 1607.74,1218.04 1609.95,1217.76 1612.15,1217.47 1614.35,1217.16 1616.55,1216.83 \n",
       "  1618.75,1216.49 1620.96,1216.13 1623.16,1215.75 1625.36,1215.35 1627.56,1214.93 1629.77,1214.5 1631.97,1214.05 1634.17,1213.58 1636.37,1213.09 1638.57,1212.59 \n",
       "  1640.78,1212.07 1642.98,1211.53 1645.18,1210.98 1647.38,1210.4 1649.59,1209.81 1651.79,1209.21 1653.99,1208.58 1656.19,1207.94 1658.39,1207.28 1660.6,1206.6 \n",
       "  1662.8,1205.91 1665,1205.2 1667.2,1204.47 1669.41,1203.72 1671.61,1202.96 1673.81,1202.18 1676.01,1201.39 1678.21,1200.58 1680.42,1199.75 1682.62,1198.9 \n",
       "  1684.82,1198.04 1687.02,1197.16 1689.23,1196.27 1691.43,1195.36 1693.63,1194.43 1695.83,1193.48 1698.03,1192.52 1700.24,1191.55 1702.44,1190.56 1704.64,1189.55 \n",
       "  1706.84,1188.53 1709.05,1187.49 1711.25,1186.43 1713.45,1185.36 1715.65,1184.28 1717.85,1183.18 1720.06,1182.06 1722.26,1180.93 1724.46,1179.79 1726.66,1178.63 \n",
       "  1728.86,1177.45 1731.07,1176.26 1733.27,1175.06 1735.47,1173.84 1737.67,1172.61 1739.88,1171.36 1742.08,1170.1 1744.28,1168.83 1746.48,1167.54 1748.68,1166.24 \n",
       "  1750.89,1164.92 1753.09,1163.6 1755.29,1162.26 1757.49,1160.9 1759.7,1159.54 1761.9,1158.16 1764.1,1156.77 1766.3,1155.37 1768.5,1153.96 1770.71,1152.54 \n",
       "  1772.91,1151.1 1775.11,1149.66 1777.31,1148.2 1779.52,1146.73 1781.72,1145.26 1783.92,1143.77 1786.12,1142.27 1788.32,1140.77 1790.53,1139.25 1792.73,1137.73 \n",
       "  1794.93,1136.19 1797.13,1134.65 1799.34,1133.1 1801.54,1131.54 1803.74,1129.98 1805.94,1128.41 1808.14,1126.83 1810.35,1125.24 1812.55,1123.65 1814.75,1122.05 \n",
       "  1816.95,1120.45 1819.16,1118.84 1821.36,1117.23 1823.56,1115.61 1825.76,1113.99 1827.96,1112.36 1830.17,1110.73 1832.37,1109.1 1834.57,1107.46 1836.77,1105.82 \n",
       "  1838.98,1104.17 1841.18,1102.53 1843.38,1100.88 1845.58,1099.23 1847.78,1097.58 1849.99,1095.94 1852.19,1094.29 1854.39,1092.64 1856.59,1090.99 1858.8,1089.35 \n",
       "  1861,1087.7 1863.2,1086.06 1865.4,1084.43 1867.6,1082.79 1869.81,1081.16 1872.01,1079.54 1874.21,1077.92 1876.41,1076.3 1878.62,1074.69 1880.82,1073.09 \n",
       "  1883.02,1071.49 1885.22,1069.9 1887.42,1068.32 1889.63,1066.75 1891.83,1065.18 1894.03,1063.62 1896.23,1062.08 1898.44,1060.54 1900.64,1059.01 1902.84,1057.49 \n",
       "  1905.04,1055.98 1907.24,1054.49 1909.45,1053 1911.65,1051.53 1913.85,1050.07 1916.05,1048.62 1918.26,1047.18 1920.46,1045.76 1922.66,1044.35 1924.86,1042.96 \n",
       "  1927.06,1041.58 1929.27,1040.22 1931.47,1038.87 1933.67,1037.53 1935.87,1036.22 1938.08,1034.91 1940.28,1033.63 1942.48,1032.36 1944.68,1031.11 1946.88,1029.87 \n",
       "  1949.09,1028.66 1951.29,1027.46 1953.49,1026.28 1955.69,1025.12 1957.89,1023.98 1960.1,1022.85 1962.3,1021.75 1964.5,1020.67 1966.7,1019.61 1968.91,1018.56 \n",
       "  1971.11,1017.54 1973.31,1016.54 1975.51,1015.55 1977.71,1014.59 1979.92,1013.64 1982.12,1012.72 1984.32,1011.81 1986.52,1010.93 1988.73,1010.07 1990.93,1009.23 \n",
       "  1993.13,1008.41 1995.33,1007.61 1997.53,1006.84 1999.74,1006.08 2001.94,1005.35 2004.14,1004.64 2006.34,1003.96 2008.55,1003.3 2010.75,1002.66 2012.95,1002.04 \n",
       "  2015.15,1001.44 2017.35,1000.87 2019.56,1000.32 2021.76,999.799 2023.96,999.297 2026.16,998.818 2028.37,998.362 2030.57,997.929 2032.77,997.519 2034.97,997.132 \n",
       "  2037.17,996.769 2039.38,996.428 2041.58,996.109 2043.78,995.814 2045.98,995.541 2048.19,995.29 2050.39,995.062 2052.59,994.856 2054.79,994.671 2056.99,994.509 \n",
       "  2059.2,994.368 2061.4,994.248 2063.6,994.149 2065.8,994.072 2068.01,994.014 2070.21,993.977 2072.41,993.961 2074.61,993.963 2076.81,993.986 2079.02,994.027 \n",
       "  2081.22,994.087 2083.42,994.165 2085.62,994.262 2087.83,994.376 2090.03,994.507 2092.23,994.655 2094.43,994.82 2096.63,995 2098.84,995.196 2101.04,995.407 \n",
       "  2103.24,995.633 2105.44,995.874 2107.65,996.131 2109.85,996.405 2112.05,996.694 2114.25,996.999 2116.45,997.32 2118.66,997.656 2120.86,998.007 2123.06,998.373 \n",
       "  2125.26,998.754 2127.47,999.149 2129.67,999.557 2131.87,999.98 2134.07,1000.42 2136.27,1000.87 2138.48,1001.33 2140.68,1001.81 2142.88,1002.3 2145.08,1002.8 \n",
       "  2147.29,1003.31 2149.49,1003.84 2151.69,1004.37 2153.89,1004.92 2156.09,1005.48 2158.3,1006.06 2160.5,1006.64 2162.7,1007.23 2164.9,1007.84 2167.11,1008.45 \n",
       "  2169.31,1009.07 2171.51,1009.71 2173.71,1010.35 2175.91,1011 2178.12,1011.67 2180.32,1012.34 2182.52,1013.02 2184.72,1013.7 2186.92,1014.4 2189.13,1015.1 \n",
       "  2191.33,1015.82 2193.53,1016.54 2195.73,1017.26 2197.94,1018 2200.14,1018.74 2202.34,1019.48 2204.54,1020.24 2206.74,1021 2208.95,1021.76 2211.15,1022.54 \n",
       "  2213.35,1023.31 2215.55,1024.1 2217.76,1024.89 2219.96,1025.68 2222.16,1026.48 2224.36,1027.28 2226.56,1028.08 2228.77,1028.89 2230.97,1029.71 2233.17,1030.52 \n",
       "  2235.37,1031.35 2237.58,1032.17 2239.78,1033 2241.98,1033.83 2244.18,1034.66 2246.38,1035.5 2248.59,1036.34 2250.79,1037.18 2252.99,1038.03 2255.19,1038.87 \n",
       "  2257.4,1039.72 2259.6,1040.57 2261.8,1041.42 2264,1042.27 2266.2,1043.13 2268.41,1043.98 2270.61,1044.84 2272.81,1045.69 2275.01,1046.55 2277.22,1047.4 \n",
       "  2279.42,1048.26 2281.62,1049.12 2283.82,1049.97 2286.02,1050.83 2288.23,1051.68 2290.43,1052.54 2292.63,1053.39 2294.83,1054.24 2297.04,1055.09 2299.24,1055.94 \n",
       "  2301.44,1056.79 2303.64,1057.64 2305.84,1058.48 2308.05,1059.32 2310.25,1060.16 2312.45,1061 2314.65,1061.84 2316.86,1062.67 2319.06,1063.51 2321.26,1064.33 \n",
       "  \n",
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       "  \"/>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:start;\" transform=\"rotate(0, 2102.3, 208.744)\" x=\"2102.3\" y=\"208.744\">u1(t)</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip2001)\" style=\"stroke:#e26f46; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
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       "  \"/>\n",
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48; text-anchor:start;\" transform=\"rotate(0, 2102.3, 269.224)\" x=\"2102.3\" y=\"269.224\">u2(t)</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function f(du,u,h,p,t)\n",
    "  x, y = u\n",
    "  α,β,γ,δ = p\n",
    "  du[1] = α*h(p,t-1)[1] - β*x*y\n",
    "  du[2] = -γ*y + δ*x*y\n",
    "end\n",
    "p = (1.5,1.0,3.0,1.0); u0 = [1.0;1.0]\n",
    "tspan = (0.0,10.0)\n",
    "_h(p,t) = ones(2)\n",
    "prob1 = DDEProblem(f,u0,_h,tspan,p)\n",
    "sol = solve(prob1)\n",
    "using Plots; plot(sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Usable from R, Python, and the Web!\n",
    "\n",
    "- diffeqr (R) : https://cran.r-project.org/web/packages/diffeqr/index.html\n",
    "- diffeqpy (Python) : https://github.com/JuliaDiffEq/diffeqpy\n",
    "- DifferentialEquations.jl Online (Web Browser): http://app.juliadiffeq.org/\n",
    "- Interact.jl + WebAssembly.jl: Compile DifferentialEquations.jl models to the browser!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## DifferentialEquations.jl has a large active developer-base\n",
    "\n",
    "#### Let us know what you need!"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Julia 1.0.0",
   "language": "julia",
   "name": "julia-1.0"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.0.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}