{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Engy-5310: Computational Continuum Transport Phenomena Fall 2021 UMass Lowell; Prof. V. F. de Almeida **05Oct21**\n",
"\n",
"# Homework 03 (05Oct21)\n",
"\n",
"$ \n",
" \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
" \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n",
" \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n",
" \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n",
" \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n",
" \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
" \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
" \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
" \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
" \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
" \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
" \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
" \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
" \\newcommand{\\fvec}{\\boldsymbol{\\mathsf{f}}}\n",
" \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
" \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
" \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
" \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
" \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
" \\DeclareMathOperator{\\rank}{rank}\n",
" \\newcommand{\\Reals}{\\mathbb{R}}\n",
" \\newcommand{\\thetavec}{\\boldsymbol{\\theta}}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Name: `your name`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Rubric for each assignment: \n",
"\n",
"| Context | Points |\n",
"| ----------------------- | ------- |\n",
"| Precision of the answer | 80% |\n",
"| Answer Markdown readability | 10% |\n",
"| Code readability | 10% |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Guidance:\n",
"\n",
"+ \n",
" Save your work frequently to a file locally to your computer.\n",
" \n",
"+ \n",
" During your work and before submitting the final version do: Kernel -> Restart & Run All, to verify your notebook runs correctly.\n",
" \n",
"+ \n",
" Save your file again.\n",
" \n",
"+ \n",
" Upload the notebook file in the Blackboard submission portal as: \n",
" \n",
" \n",
" **lastname-firstname-labwork-xx.ipynb**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Table of Assignments\n",
"* [Assignment 1 (30 pts)](#a1) Function approximation with constrained end-points.\n",
" - [1.1)](#a11)(5 pts) Generate the target function.\n",
" - [1.2)](#a12)(10 pts) Compute parameters for a given error level.\n",
" - [1.3)](#a13)(15 pts) Using the same basis functions, approximate the target function continuously ($m\\rightarrow\\infty$) and constrain the end points.\n",
"* [Assignment 2 (65 pts)](#a2) Function approximation with constrained end-point derivatives.\n",
" - [2.1)](#a21)(35 pts) Constrained Fourier basis function approximation.\n",
" - [2.2)](#a22)(30 pts) Demonstrate why the approximation results for the end point derivatives can't be improved.\n",
"* [Assignment 3 (5 pts)](#a3) .\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Assignment 1 (30 pts)](#toa)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [1.1)](#toa)(5 pts) Generate the following piecewise linear function on these shape points:\n",
"
\n",
"\n",
" $\\{(-8,1),(-6,10),(-5,-7),(0,-5),(1,9),(2,-8),(3,28),(5,-23),(7,12),(9,1),(10,10),(12,15),(14,18),(15,10)\\}$.\n",
""
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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