#!/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.