This textbook gives an introduction to Partial Differential Equations
(PDEs), for any reader wishing to learn and understand the basic
concepts, theory, and solution techniques of elementary PDEs. The only
prerequisite is an undergraduate course in Ordinary Differential
Equations. This work contains a comprehensive treatment of the standard
second-order linear PDEs, the heat equation, wave equation, and
Laplace's equation. First-order and some common nonlinear PDEs arising
in the physical and life sciences, with their solutions, are also
covered.This textbook includes an introduction to Fourier series and
their properties, an introduction to regular Sturm-Liouville boundary
value problems, special functions of mathematical physics, a treatment
of nonhomogeneous equations and boundary conditions using methods such
as Duhamel's principle, and an introduction to the finite difference
technique for the numerical approximation of solutions. All results have
been rigorously justified or precise references to justifications in
more advanced sources have been cited. Appendices providing a background
in complex analysis and linear algebra are also included for readers
with limited prior exposure to those subjects.The textbook includes
material from which instructors could create a one- or two-semester
course in PDEs. Students may also study this material in preparation for
a graduate school (masters or doctoral) course in PDEs.
