\(\newcommand{\bx}{\textbf{x}} \newcommand{\bo}{\textbf{0}} \newcommand{\bv}{\textbf{v}} \newcommand{\bu}{\textbf{u}} \newcommand{\bq}{\textbf{q}} \newcommand{\by}{\textbf{y}} \newcommand{\bb}{\textbf{b}} \newcommand{\ba}{\textbf{a}} \newcommand{\grad}{\boldsymbol{\nabla}} \newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\pdd}[2]{\frac{\partial^2 #1}{\partial #2^2}} \newcommand{\pddm}[3]{\frac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\deriv}[2]{\frac{d #1}{d #2}} \newcommand{\lt}{ < } \newcommand{\gt}{ > } \newcommand{\amp}{ & } \)

Chapter6Numerical Differential Equations — ODEs and PDEs

In this final chapter we explore some of the numerical techniques associated with approximating solutions to ordinary and partial differential equations. The Taylor approximations that we have used in the past will come in handy; as will your finely tuned coding skills. We will cover the methods for ordinary differential equations fairly quickly since some of the techniques (like Euler's method) have been explored in other classes.