#!/usr/bin/env python # coding: utf-8 # Advanced Mathematics for Nuclear Chemical Engineering August 2020 UMass Lowell; Prof. V. F. de Almeida **07Aug2020** # # # 06. Integro-Differential Equations # $ # \newcommand{\Amtrx}{\boldsymbol{\mathsf{A}}} # \newcommand{\Bmtrx}{\boldsymbol{\mathsf{B}}} # \newcommand{\Mmtrx}{\boldsymbol{\mathsf{M}}} # \newcommand{\Imtrx}{\boldsymbol{\mathsf{I}}} # \newcommand{\Pmtrx}{\boldsymbol{\mathsf{P}}} # \newcommand{\Lmtrx}{\boldsymbol{\mathsf{L}}} # \newcommand{\Umtrx}{\boldsymbol{\mathsf{U}}} # \newcommand{\Jmtrx}{\boldsymbol{\mathsf{J}}} # \newcommand{\Smtrx}{\boldsymbol{\mathsf{S}}} # \newcommand{\Xmtrx}{\boldsymbol{\mathsf{X}}} # \newcommand{\Kmtrx}{\boldsymbol{\mathsf{K}}} # \newcommand{\xvec}{\boldsymbol{x}} # \newcommand{\avec}{\boldsymbol{\mathsf{a}}} # \newcommand{\bvec}{\boldsymbol{\mathsf{b}}} # \newcommand{\cvec}{\boldsymbol{\mathsf{c}}} # \newcommand{\rvec}{\boldsymbol{\mathsf{r}}} # \newcommand{\mvec}{\boldsymbol{\mathsf{m}}} # \newcommand{\gvec}{\boldsymbol{\mathsf{g}}} # \newcommand{\zerovec}{\boldsymbol{\mathsf{0}}} # \newcommand{\norm}[1]{\bigl\lVert{#1}\bigr\rVert} # \newcommand{\abs}[1]{\left\lvert{#1}\right\rvert} # \newcommand{\transpose}[1]{{#1}^\top} # \DeclareMathOperator{\rank}{rank} # \DeclareMathOperator{\gradx}{\nabla\!_{\xvec}} # \newcommand{\Kcal}{\mathcal{K}} # \newcommand{\Fcal}{\mathcal{F}} # \newcommand{\Kcalvec}{\boldsymbol{\mathcal{K}}} # \newcommand{\Fcalvec}{\boldsymbol{\mathcal{F}}} # \newcommand{\epsvec}{\boldsymbol{\varepsilon}} # $ # --- # ## Table of Contents # * [Analytical Methods of Solution](#ams) # - Approximate analytical integration methods for time-dependent, one-dimensional spatial variable. # - Approximate analytical integration methods for two-dimensional spatial variables. # --- # ## [Analytical Methods of Solution](#toc) # # Revise standard analytical methods of solution of integro-differential equations from past courses in nuclear and chemical engineering. Only time-dependent equations with one-dimensional spatial variable or a total of two spatial varialbles, should be covered. These methods typically result in approximate solutions in terms of known mathematical functions.