ABSTRACT
In this chapter we solve several, elementary, partial differential equations generated by mathematical physics. We start with first-order transport equations, first using the built in Mathematica command DSolve and then show how we may combine this with the method of characteristics to solve more general first-order equations. In later sections we consider the heat, potential and wave equations using the method of separation of variables. The potential equation, also known as Laplace’s equation is solved in two and three space variables. We make frequent use of the Mathematica command DSolve to find the general form of a solution. For second order equations we mostly use a separation of variables technique; however, there is a built in Mathematica command for solving Laplace’s equation. Whereas, we want to show the possibilities to use Mathematica directly, the purpose of this book is to study mathematics and to use the mathematics to help you write your own programs. The use of writing programs is meant to reinforce the mathematical ideas.
