ABSTRACT
This chapter provides an overview of the applications of partial differential equations (PDEs), and introduces the reader to some elementary techniques, such as separation of variables. It gives the reader a perspective on the uses of PDEs in various scientific applications, such as gravitation, electrostatics, thermodynamics, acoustics, and minimal soap film surfaces. The chapter contrastes the studies of ODEs and PDEs, with regard to the differences in the typical forms for general solutions. It illustrates how side conditions are used to extract particular solutions from general ones. Nonlinear equations are often approximated by linear equations which hopefully yield solutions that are close to the corresponding solutions of the nonlinear equations. Ideally, one would like to have a general technique that could be used to find all of the solutions of an arbitrary PDE, or at least a relevant solution that satisfies certain initial/boundary conditions.
