{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Advanced Mathematics for Nuclear Chemical Engineering August 2020 UMass Lowell; Prof. V. F. de Almeida **07Aug2020**\n", "\n", "# 05. Partial Differential Equations\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{\\Jmtrx}{\\boldsymbol{\\mathsf{J}}}\n", " \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n", " \\newcommand{\\Xmtrx}{\\boldsymbol{\\mathsf{X}}}\n", " \\newcommand{\\Kmtrx}{\\boldsymbol{\\mathsf{K}}}\n", " \\newcommand{\\xvec}{\\boldsymbol{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{\\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{\\abs}[1]{\\left\\lvert{#1}\\right\\rvert}\n", " \\newcommand{\\transpose}[1]{{#1}^\\top}\n", " \\DeclareMathOperator{\\rank}{rank}\n", " \\DeclareMathOperator{\\gradx}{\\nabla\\!_{\\xvec}}\n", " \\newcommand{\\Kcal}{\\mathcal{K}}\n", " \\newcommand{\\Fcal}{\\mathcal{F}}\n", " \\newcommand{\\Kcalvec}{\\boldsymbol{\\mathcal{K}}}\n", " \\newcommand{\\Fcalvec}{\\boldsymbol{\\mathcal{F}}}\n", " \\newcommand{\\epsvec}{\\boldsymbol{\\varepsilon}}\n", "$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Table of Contents\n", "* [Analytical Methods of Solution](#ams)\n", " - Analytical integration methods for time-dependent, one-dimensional spatial variable.\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## [Analytical Methods of Solution](#toc)\n", "\n", "Revise standard analytical methods of solution of partial differential equations from past courses in nuclear and chemical engineering. Only time-dependent equations with one-dimensional spatial variable should be covered. Those methods result in closed solutions in terms of known mathematical functions." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false } }, "nbformat": 4, "nbformat_minor": 2 }