This free text concentrates on mathematical concepts rather than on details of calculations, which are often done with software, such as Maple or Mathematica.

## Book Description

It is not necessary to have experience with Maple or Mathematica in order to read this text, nor is it the goal of this text to teach software, but there are links in the text to Maple worksheets and Mathematica notebooks, which perform calculations and provide some supplementary instructive material.

## Table of Contents

- The geometry of functions
- Fourier series. Introduction
- Calculating Fourier series
- Differentiating Fourier series
- Notes on a vibrating string
- Traveling waves
- Mathematics of hot rods
- PDEs in space
- PDEs on a disk
- Great balls of PDEs
- Hunting for eigenvalues
- Geometry and integral operators
- Solving Y = KY + f
- Ordinary differential operators
- Finding Green functions for ODEs
- Green functions, Fourier series, and eigenfunctions
- Partial differential operators – classification and adjoints
- The free Green function and the method of images
- The fundamental solution of the heat equation
- Using conformal mapping to construct Green functions
- Some advanced topics