{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# SageMath físicos\n", "***\n", "Rogério T. C." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**SageMath** (ou simplesmente Sage) é um sistema de computação algébrica. Dentre outras, algumas vantágens de usar sistemas desse tipo são:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Você pode se concentrar mais nas idéias (modelo, formulação, teoria) e menos nas \"contas\";" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Os resultados estendidos, generalizados e analisados com facilidade;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Você pode explorar a estrutura matemática em torno do seu problema, o Sage é ótimo para isso;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Seus resultados podem ser compartilhados de uma forma reproduzível;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Depois de investir algum tempo aprendendo o básico, você poderá resolver problema de forma muito mais rápido e com mais ferramentas;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Você só precisa saber um conjunto básico de comandos e sintaxe, e para todo o restante pode usar os recursos de ajuda e a documentação;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Tópicos da aula de hoje" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "1. Pré-documento;\n", "2. Operações básicas;\n", "3. Variáveis simbólicas;\n", "4. Expressões simbólicas;\n", "5. Equações, inequações e sistemas\n", "6. Ferramentas de cálculo\n", "7. Substituições em expressões simbólicas\n", "8. Equações diferenciais ordinárias" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Aula I" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 1. Pré-documento" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Você pode fazer o jupyter exibir as equações no formato $\\LaTeX{}$ digitando `%display latex` em uma célula." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "%display latex # outras opções são plane, ascii_art e unicode_art" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "reset() #inicializa todas as variáveis" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2. Operações Básicas" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "No Sage as operações básicas com números reais, complexos, racionais, etc., são realizadas como nas calculadoras científicas. Frações e raízes são automaticamente simplificadas" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{21}{10}\n", "\\end{math}" ], "text/plain": [ "21/10" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "15/25+3/2" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, \\sqrt{5}}{\\pi}\n", "\\end{math}" ], "text/plain": [ "2*sqrt(5)/pi" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sqrt(20)/pi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aproximação numérica" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}4.47213595499958\n", "\\end{math}" ], "text/plain": [ "4.47213595499958" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sqrt(20).n()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}4.47213595499958\n", "\\end{math}" ], "text/plain": [ "4.47213595499958" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sqrt(20.0)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Algumas operações e funções básicas do Sage:\n", "\n", "|Operação|Sintáxe|\n", "|:-:|:-:|\n", "|4 operações | `a+b, a-b, a*b, a/b`|\n", "|Potêmcia | `a**b ou a^b`|\n", "|Raiz quadrada | `sqrt(a)`|\n", "|Divisão inteira | `a//b`|\n", "|Resto na divisão | `a%b`|\n", "|Fatorial | `factorial(a)`|\n", "|Coeficiente binômial $\\begin{pmatrix} a\\\\ b\\end{pmatrix}$ | `binomial(a,b)`|\n", "|Parte inteira | `floor(a)`|\n", "|Valor absoluto | `abs(a)`|\n", "|Aproximação numérica | `N(a) ou a.n()`|" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 3. Variáveis simbólicas" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Existem dois tipos básicos de variáveis no sage:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* As variáveis simbólicas, usadas nos cálculos simbólicos;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* Variáveis python, que são usadas para guardas alguma informação na memória. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Variáveis simbólicas precisam ser declaradas. Exceto `x`, que já vem pré-declarada." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(u, y, w, a, b, c\\right)\n", "\\end{math}" ], "text/plain": [ "(u, y, w, a, b, c)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('u y w a b c') " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Uma lista de varáveis simbólicas indexadas pode ser criada com:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(x_{0}, x_{1}, x_{2}, x_{3}\\right)\n", "\\end{math}" ], "text/plain": [ "(x0, x1, x2, x3)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = var('x',n=4)\n", "X" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x_{1}\n", "\\end{math}" ], "text/plain": [ "x1" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Você pode tammbém definir o domínio e um nome $\\LaTeX{}$ para variáveis simbólicas." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\bar{\\alpha}}\n", "\\end{math}" ], "text/plain": [ "alp_bar" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('alp_bar', latex_name=r'\\bar{\\alpha}', domain='real')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\bar{\\alpha}}\n", "\\end{math}" ], "text/plain": [ "alp_bar" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alp_bar" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Variáveis simbólicas são usadas, por exemplo, para declarar funções." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}u \\ {\\mapsto}\\ \\cos\\left(u\\right)^{6} + \\sin\\left(u\\right)^{6} + 3 \\, \\cos\\left(u\\right)^{2} \\sin\\left(u\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "u |--> cos(u)^6 + sin(u)^6 + 3*cos(u)^2*sin(u)^2" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(u)=cos(u)^6 + sin(u)^6 + 3 * sin(u)^2 * cos(u)^2\n", "f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Código $\\LaTeX$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\cos\\left(u\\right)^{6} + \\sin\\left(u\\right)^{6} + 3 \\, \\cos\\left(u\\right)^{2} \\sin\\left(u\\right)^{2}\n" ] } ], "source": [ "print(latex(f(u)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Assim como Python, o Sage usa o paradigma de orientação ao objeto. Se você digitar `.` após o nome de um objeto e apertar a tecla Tab, será exibda uma lista de métodos associados a este objeto." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "* A última saída é armazenada na variável `_` \n", "* Penúltima em `__` \n", "* Antepenúltima `___`" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}u \\ {\\mapsto}\\ \\cos\\left(u\\right)^{6} + \\sin\\left(u\\right)^{6} + 3 \\, \\cos\\left(u\\right)^{2} \\sin\\left(u\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "u |--> cos(u)^6 + sin(u)^6 + 3*cos(u)^2*sin(u)^2" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Um `?` após o nome de uma função exibe uma descrição da mesma, geralmente com alguns exemplos." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 4. Expressões simbólicas" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Expressões simbólicas podem ser manipuladas de várias formas" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(x + y\\right)} {\\left(x + 1\\right)}^{2}\n", "\\end{math}" ], "text/plain": [ "(x + y)*(x + 1)^2" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = (x+y)*(x+1)^2; p" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} + x^{2} y + 2 \\, x^{2} + 2 \\, x y + x + y\n", "\\end{math}" ], "text/plain": [ "x^3 + x^2*y + 2*x^2 + 2*x*y + x + y" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p2 = p.expand(); p2" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} + x^{2} {\\left(y + 2\\right)} + x {\\left(2 \\, y + 1\\right)} + y\n", "\\end{math}" ], "text/plain": [ "x^3 + x^2*(y + 2) + x*(2*y + 1) + y" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p2.collect(x) #potências da x" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(x + y\\right)} {\\left(x + 1\\right)}^{2}\n", "\\end{math}" ], "text/plain": [ "(x + y)*(x + 1)^2" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p2.factor()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Identidades trigonômétricas podem ser utilizadas com `.expand_trig()`" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(y\\right) \\sin\\left(x\\right) + \\cos\\left(x\\right) \\sin\\left(y\\right)\n", "\\end{math}" ], "text/plain": [ "cos(y)*sin(x) + cos(x)*sin(y)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(x+y).expand_trig()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\tanh\\left(x\\right) + \\tanh\\left(y\\right)}{\\tanh\\left(x\\right) \\tanh\\left(y\\right) + 1}\n", "\\end{math}" ], "text/plain": [ "(tanh(x) + tanh(y))/(tanh(x)*tanh(y) + 1)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tanh(x+y).expand_trig()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Ou simplificadas usando `trig_simplify()`" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(u\\right)^{6} + \\sin\\left(u\\right)^{6} + 3 \\, \\cos\\left(u\\right)^{2} \\sin\\left(u\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "cos(u)^6 + sin(u)^6 + 3*cos(u)^2*sin(u)^2" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(u)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-6 \\, \\cos\\left(u\\right)^{5} \\sin\\left(u\\right) + 6 \\, \\cos\\left(u\\right) \\sin\\left(u\\right)^{5} + 6 \\, \\cos\\left(u\\right)^{3} \\sin\\left(u\\right) - 6 \\, \\cos\\left(u\\right) \\sin\\left(u\\right)^{3}\n", "\\end{math}" ], "text/plain": [ "-6*cos(u)^5*sin(u) + 6*cos(u)*sin(u)^5 + 6*cos(u)^3*sin(u) - 6*cos(u)*sin(u)^3" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(u).diff()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1\n", "\\end{math}" ], "text/plain": [ "1" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(u).trig_simplify()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(u).diff().trig_simplify()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Manipulação simbólica de polinômios:\n", "\n", "Função | Comando\n", ":--- | :---\n", "expandir | `expand()`\n", "polinômio em `x` | `collect(x)`\n", "Fatorar | `factor()`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Funções trigonométricas:\n", "\n", "Função | Comando\n", ":--- | :---\n", "Simplificação | `trig_simplify()`\n", "Linearização | `reduce_trig()`\n", "Expansão | `expand_trig()`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Raízes e frações:\n", "\n", "Função | Comando\n", ":--- | :---\n", "Somar frações com o mesmo denominador | `combine()`\n", "Rotina de simplificações com raízes e frações(muito útil) | `canonicalize_radical()`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Geral:\n", "\n", "Função | Comando\n", ":--- | :---\n", "Simplificação | `simplify()`\n", "Simplificação completa | `full_simplify()`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 5. Equações, inequações e sistemas" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Equações podem ser definidas por expressões simbólicas e guardadas em variáveis python e manipuladas." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}y^{2} - \\frac{2 \\, y}{\\cos\\left(\\phi\\right)} + \\frac{5}{\\cos\\left(\\phi\\right)^{2}} - 4 = 0\n", "\\end{math}" ], "text/plain": [ "y^2 - 2*y/cos(phi) + 5/cos(phi)^2 - 4 == 0" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('phi')\n", "eq0 = y**2 - 2/cos(phi)*y + 5/cos(phi)**2 - 4 == 0; eq0" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "
\n", "Note que equações são definidas pelo operador `==`\n", "
" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}y^{2} \\cos\\left(\\phi\\right)^{2} - 2 \\, y \\cos\\left(\\phi\\right) - 4 \\, \\cos\\left(\\phi\\right)^{2} + 5 = 0\n", "\\end{math}" ], "text/plain": [ "y^2*cos(phi)^2 - 2*y*cos(phi) - 4*cos(phi)^2 + 5 == 0" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1=(eq0*cos(phi)^2).expand(); eq1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para extrair os lados da equação, `.lhs()` ou `.rhs()`" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}y^{2} \\cos\\left(\\phi\\right)^{2} - 2 \\, y \\cos\\left(\\phi\\right) - 4 \\, \\cos\\left(\\phi\\right)^{2} + 5\n", "\\end{math}" ], "text/plain": [ "y^2*cos(phi)^2 - 2*y*cos(phi) - 4*cos(phi)^2 + 5" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1.lhs()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1.rhs()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Equações também podem ser resolvidas diretamente usando o comando `solve`" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y = -\\frac{2 \\, \\sqrt{\\cos\\left(\\phi\\right)^{2} - 1} - 1}{\\cos\\left(\\phi\\right)}, y = \\frac{2 \\, \\sqrt{\\cos\\left(\\phi\\right)^{2} - 1} + 1}{\\cos\\left(\\phi\\right)}\\right]\n", "\\end{math}" ], "text/plain": [ "[y == -(2*sqrt(cos(phi)^2 - 1) - 1)/cos(phi), y == (2*sqrt(cos(phi)^2 - 1) + 1)/cos(phi)]" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq1,y)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\phi = \\pi - \\arccos\\left(-\\frac{y}{y^{2} - 4} + \\frac{2 \\, \\sqrt{-y^{2} + 5}}{y^{2} - 4}\\right), \\phi = \\arccos\\left(\\frac{y}{y^{2} - 4} + \\frac{2 \\, \\sqrt{-y^{2} + 5}}{y^{2} - 4}\\right)\\right]\n", "\\end{math}" ], "text/plain": [ "[phi == pi - arccos(-y/(y^2 - 4) + 2*sqrt(-y^2 + 5)/(y^2 - 4)), phi == arccos(y/(y^2 - 4) + 2*sqrt(-y^2 + 5)/(y^2 - 4))]" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol=solve(eq1,phi); sol" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\phi = \\pi - \\arccos\\left(-\\frac{y}{y^{2} - 4} + \\frac{2 \\, \\sqrt{-y^{2} + 5}}{y^{2} - 4}\\right)\n", "\\end{math}" ], "text/plain": [ "phi == pi - arccos(-y/(y^2 - 4) + 2*sqrt(-y^2 + 5)/(y^2 - 4))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol[0]" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\pi - \\arccos\\left(-\\frac{y}{y^{2} - 4} + \\frac{2 \\, \\sqrt{-y^{2} + 5}}{y^{2} - 4}\\right)\n", "\\end{math}" ], "text/plain": [ "pi - arccos(-y/(y^2 - 4) + 2*sqrt(-y^2 + 5)/(y^2 - 4))" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol[0].rhs()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\pi - \\arccos\\left(-\\frac{y}{y^{2} - 4} + \\frac{2 \\, \\sqrt{-y^{2} + 5}}{y^{2} - 4}\\right)\n" ] } ], "source": [ "print(latex(sol[0].rhs()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Você pode assumir expressões simbólicas que serão usadas nos cálculos simbólicos internamente com a função `assume(expressão)`" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "assume(phi^2<20)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\verb|alp_bar|\\phantom{\\verb!x!}\\verb|is|\\phantom{\\verb!x!}\\verb|real|, \\phi^{2} < 20\\right]\n", "\\end{math}" ], "text/plain": [ "[alp_bar is real, phi^2 < 20]" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assumptions()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 5.1 Sistemas de equações e inequações" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "O `solve` também resolve sistemas de equações ou inequações " ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(x^{2} + x y + 2 = 0, y^{2} = {\\left(x + y\\right)} x\\right)\n", "\\end{math}" ], "text/plain": [ "(x^2 + x*y + 2 == 0, y^2 == (x + y)*x)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq2 = x^2 + x*y + 2 == 0\n", "eq3 = y^2 == x*(x+y)\n", "(eq2, eq3)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[x = -\\frac{1}{2} i \\, \\sqrt{10} + \\frac{1}{2} i \\, \\sqrt{2}, y = -i \\, \\sqrt{2}\\right], \\left[x = \\frac{1}{2} i \\, \\sqrt{10} + \\frac{1}{2} i \\, \\sqrt{2}, y = -i \\, \\sqrt{2}\\right], \\left[x = -\\frac{1}{2} i \\, \\sqrt{10} - \\frac{1}{2} i \\, \\sqrt{2}, y = i \\, \\sqrt{2}\\right], \\left[x = \\frac{1}{2} i \\, \\sqrt{10} - \\frac{1}{2} i \\, \\sqrt{2}, y = i \\, \\sqrt{2}\\right]\\right]\n", "\\end{math}" ], "text/plain": [ "[[x == -1/2*I*sqrt(10) + 1/2*I*sqrt(2), y == -I*sqrt(2)], [x == 1/2*I*sqrt(10) + 1/2*I*sqrt(2), y == -I*sqrt(2)], [x == -1/2*I*sqrt(10) - 1/2*I*sqrt(2), y == I*sqrt(2)], [x == 1/2*I*sqrt(10) - 1/2*I*sqrt(2), y == I*sqrt(2)]]" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sols = solve((eq2, eq3), x, y)\n", "sols" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = -\\frac{1}{2} i \\, \\sqrt{10} + \\frac{1}{2} i \\, \\sqrt{2}, y = -i \\, \\sqrt{2}\\right]\n", "\\end{math}" ], "text/plain": [ "[x == -1/2*I*sqrt(10) + 1/2*I*sqrt(2), y == -I*sqrt(2)]" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sols[0]" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = -\\frac{1}{2} i \\, \\sqrt{10} + \\frac{1}{2} i \\, \\sqrt{2}\n", "\\end{math}" ], "text/plain": [ "x == -1/2*I*sqrt(10) + 1/2*I*sqrt(2)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sols[0][0]" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[x < -\\frac{1}{2} \\, \\sqrt{5} - \\frac{1}{2}\\right], \\left[x > \\frac{1}{2} \\, \\sqrt{5} - \\frac{1}{2}\\right]\\right]\n", "\\end{math}" ], "text/plain": [ "[[x < -1/2*sqrt(5) - 1/2], [x > 1/2*sqrt(5) - 1/2]]" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(x^2+x-1 > 0, x)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 5.2 Solução numérica" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Em alguns casos o solve não consegue encontar uma solução para a equação." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left(3 \\, x\\right) + \\sin\\left(2 \\, x\\right) + \\sin\\left(x\\right) = 0\n", "\\end{math}" ], "text/plain": [ "sin(3*x) + sin(2*x) + sin(x) == 0" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr = sin(x) + sin(2 * x) + sin(3 * x)==0;expr" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\sin\\left(3 \\, x\\right) = -\\sin\\left(2 \\, x\\right) - \\sin\\left(x\\right)\\right]\n", "\\end{math}" ], "text/plain": [ "[sin(3*x) == -sin(2*x) - sin(x)]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(expr, x)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Nesses casos podemos usar a função `find_root`" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "A função `find_root(equação, min, max)` procura solução numérica para a equação no intervalo entre min e max. " ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2.0943951023931957\n", "\\end{math}" ], "text/plain": [ "2.0943951023931957" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_root(expr,.1,pi)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Nesse caso particular, uma solução analítica poderia ser obtida simplificando a equação" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, {\\left(2 \\, \\cos\\left(x\\right) + 1\\right)} \\cos\\left(x\\right) \\sin\\left(x\\right) = 0\n", "\\end{math}" ], "text/plain": [ "2*(2*cos(x) + 1)*cos(x)*sin(x) == 0" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr2 = expr.simplify_trig().factor(); expr2" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = 0, x = \\frac{2}{3} \\, \\pi, x = \\frac{1}{2} \\, \\pi\\right]\n", "\\end{math}" ], "text/plain": [ "[x == 0, x == 2/3*pi, x == 1/2*pi]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(expr2, x)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left(3 \\, x\\right) + \\sin\\left(2 \\, x\\right) + \\sin\\left(x\\right)\n", "\\end{math}" ], "text/plain": [ "sin(3*x) + sin(2*x) + sin(x)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr.lhs()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(expr.lhs(),(x,0,pi), gridlines=True)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Note que existem mais sluções do que o que o `find_root` encontrou. Ele mostra a primeira que encontra. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Poderíamos encontar a outra restringindo o intervalo (min, max)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.570796326794898\n", "\\end{math}" ], "text/plain": [ "1.570796326794898" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_root(expr,.1,pi/2+.1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Função | Sintáxe\n", ":--- | ---\n", "Solução simbólica | `solve(equação, variável)`\n", "Solução numérica | `find_root(equação, min, manx)`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercícios" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Defina um polinômio de grau 2 na forma $p(x) = ax^2+bx+c$. Lembre-se de definir as variáveis simbólicas antes. Agora use o solve para encontrar as soluções $p(x)=0$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 6. Ferramentas de cálculo" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 6.1 Derivadas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simples" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, x \\cos\\left(x^{2}\\right)\n", "\\end{math}" ], "text/plain": [ "2*x*cos(x^2)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(sin(x^2),x)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "de ordem superior" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-8 \\, x^{3} \\cos\\left(x^{2}\\right) - 12 \\, x \\sin\\left(x^{2}\\right)\n", "\\end{math}" ], "text/plain": [ "-8*x^3*cos(x^2) - 12*x*sin(x^2)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(sin(x^2), x,3)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "parcial" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x y^{2} + e^{\\left(-x\\right)} + \\sin\\left(x^{2}\\right)\n", "\\end{math}" ], "text/plain": [ "x*y^2 + e^(-x) + sin(x^2)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h(x,y) = x*y^2 + sin(x^2) + e^(-x); h(x,y)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}y^{2} + 2 \\, x \\cos\\left(x^{2}\\right) - e^{\\left(-x\\right)}\n", "\\end{math}" ], "text/plain": [ "y^2 + 2*x*cos(x^2) - e^(-x)" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(h(x,y), x)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, x y\n", "\\end{math}" ], "text/plain": [ "2*x*y" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(h(x,y), y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 6.2 Integrais" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "g(x) = 1/(1+x^2)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\int_{-\\infty}^{+\\infty} \\frac{1}{x^{2} + 1}\\,{d x}\n", "\\end{math}" ], "text/plain": [ "integrate(1/(x^2 + 1), x, -Infinity, +Infinity)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integral(g(x),x, -infinity, infinity,hold=True)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\pi\n", "\\end{math}" ], "text/plain": [ "pi" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integral(g(x),x, -infinity, infinity)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r - \\frac{2 \\, G M \\log\\left(r\\right)}{c^{2}}\n", "\\end{math}" ], "text/plain": [ "r - 2*G*M*log(r)/c^2" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('G M r c')\n", "integrate(1-2*G*M/(c^2*r), r)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, G M}{c^{2} r} + 1\n", "\\end{math}" ], "text/plain": [ "-2*G*M/(c^2*r) + 1" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(_,r)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 6.3 Integração numérica" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Para calcular numericamente uma integral usamos a função `integral_numerical`." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Essa função retorna um par: " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * o primeiro valor é a aproximação da integral;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * o segundo uma estimativa do erro correspondente." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0.946083070367183, 1.0503632079297087 \\times 10^{-14}\\right)\n", "\\end{math}" ], "text/plain": [ "(0.946083070367183, 1.0503632079297087e-14)" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integral_numerical(sin(x)/x, 0, 1)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\operatorname{Si}\\left(1\\right)\n", "\\end{math}" ], "text/plain": [ "sin_integral(1)" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integral(sin(x)/x,x, 0, 1)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.946083070367183\n", "\\end{math}" ], "text/plain": [ "0.946083070367183" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integral(sin(x)/x,x, 0, 1).n()" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "sin_integral?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 6.4 Séries de Taylor" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1\n", "\\end{math}" ], "text/plain": [ "1" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taylor(f(x), x, 0, 3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Função | Sintáxe\n", ":-- |:--\n", "Limite | `lim(f(x),x=a)` ou `limit(f(x),x=a)`\n", "Derivada | `diff(f(x), x)` ou `f(x).diff()`\n", "n-ésima derivada | `diff(f(x), x, n)`\n", "Integral indefinida | `integral(f(x), x)`\n", "Integral definida | `integral(f(x), x, lim_inf, lim_sup)`\n", "Integral numérica | `integral_numerical(f(x), lim_inf, lim_sup)`\n", "Série de Taylor | `taylor(f(x), x, x_0, ordem)`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. Substituições em expressões simbólicas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Uma funcionalidade muito útil em cálculos simbólicos é a substituição de exprssões com o método `.subs()`." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}A + B\n", "\\end{math}" ], "text/plain": [ "A + B" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('A B C D')\n", "a = A+B;a" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}B + D\n", "\\end{math}" ], "text/plain": [ "B + D" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.subs(A==D)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}A x^{2} + B x + C\n", "\\end{math}" ], "text/plain": [ "A*x^2 + B*x + C" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = A*x^2+B*x+C;f(x)" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{2} + 5 \\, x + 9\n", "\\end{math}" ], "text/plain": [ "x^2 + 5*x + 9" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x).subs(A==1,B==5,C==9)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, A x + B + \\cos\\left(x\\right)\n", "\\end{math}" ], "text/plain": [ "2*A*x + B + cos(x)" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = diff(f(x),x)+cos(x);b" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, A x + B + 2\n", "\\end{math}" ], "text/plain": [ "2*A*x + B + 2" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.subs(cos(x)==2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos introduzir funções com expressão não definida" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}h\\left(x\\right)\n", "\\end{math}" ], "text/plain": [ "h(x)" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = function('h')(x);h" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, {\\left(9 \\, A x^{2} + 3 \\, B x + C\\right)}^{2} + \\frac{\\partial^{2}}{(\\partial x)^{2}}h\\left(x\\right)\n", "\\end{math}" ], "text/plain": [ "2*(9*A*x^2 + 3*B*x + C)^2 + diff(h(x), x, x)" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = diff(h(x),x,2)+2*f(3*x)^2;c" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, {\\left(9 \\, A x^{2} + 3 \\, B x + C\\right)}^{2} + \\frac{x}{\\pi}\n", "\\end{math}" ], "text/plain": [ "2*(9*A*x^2 + 3*B*x + C)^2 + x/pi" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.subs(diff(h(x),x,2)==x/pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8. Equações diferenciais ordinárias" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}y\\left(x\\right)\n", "\\end{math}" ], "text/plain": [ "y(x)" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = function('y')(x);y" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial x}y\\left(x\\right) = -\\frac{2 \\, x - \\cos\\left(y\\left(x\\right)\\right)}{x \\sin\\left(y\\left(x\\right)\\right) + y\\left(x\\right)}\n", "\\end{math}" ], "text/plain": [ "diff(y(x), x) == -(2*x - cos(y(x)))/(x*sin(y(x)) + y(x))" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ed_1 = diff(y,x) == (cos(y)-2*x)/(y+x*sin(y)); ed_1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lembrando que para resolver equações diferenciais usamos `desolve(equação, dvar, ivar=t)`, onde `dvar` é a variável dependente e `ivar=t` indica que a variável independente e $t$" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{2} - x \\cos\\left(y\\left(x\\right)\\right) + \\frac{1}{2} \\, y\\left(x\\right)^{2} = C\n", "\\end{math}" ], "text/plain": [ "x^2 - x*cos(y(x)) + 1/2*y(x)^2 == _C" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol_ed = desolve(ed_1, y); sol_ed" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos plotar a função usando o `implicit_plot`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O comando `implicit_plot` recebe uma função de duas variáveis como entrada, $f(x, y)$, e plota a curva $f(x, y) = 0$ sobre os intervalo de $x$ e y especificados. Sintáxe `implicit_plot(f(x,y),(x,xmin,xmax),(y,ymin,ymax), *opções)`" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, u^{2} + x^{2} - x \\cos\\left(u\\right)\n", "\\end{math}" ], "text/plain": [ "1/2*u^2 + x^2 - x*cos(u)" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('u')\n", "sol_ed2 = sol_ed.lhs().subs(y(x)==u);sol_ed2" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_sol = implicit_plot(sol_ed2, (x,-.5,1), (u,-.7,.7), color=(0,.5,1), axes_labels=['$x$','$u$']); plot_sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Com campo" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_campos = plot_slope_field(ed_1.rhs().subs({y(x):u}), (x,-1.5,2), (u,-1.5,1.5));plot_campos" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_sol+plot_campos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercícios" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Determine o valor de $\\frac{\\partial f}{\\partial u}(0,1,1)$, para \n", "$$\n", "f(s,t,u)=\\frac{s+tu}{\\sqrt{s^2+t^2+u^2}}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Dadas as equações de transformação de coordenadas cartesianas para esféficas, já definidas abaixo, manipule simbolicamente estas equações de modo a transformação inversa. Isto é, $r(x,y,z), \\theta(x,y,z)$ e $\\phi(x,y,z)$." ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [], "source": [ "var('y z r theta phi')\n", "eqx = x == r*sin(theta)*cos(phi)\n", "eqy = y == r*sin(theta)*sin(phi)\n", "eqz = z == r*cos(theta)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Seja $g$ a aceleração da gravidade na superfície da Terra. Em termos da teoria de Newton, se $R$ é o raio da terra e $M$ sua massa, \n", "$$g = \\frac{GM}{R^2}.$$ \n", "Determine a expansão de até terceira ordem para a modificação em $g$ a uma altura $h$ acima da superfície da terra." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.2", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }