This book teaches the basic methods of partial differential equations
and introduces related important ideas associated with the analysis of
numerical methods for those partial differential equations. Standard
topics such as separation of variables, Fourier analysis, maximum
principles, and energy estimates are included. Numerical methods are
introduced in parallel to the classical theory. The numerical
experiments are used to illustrate properties of differential equations,
and a theory for finite difference approximations is developed. The
text would be suitable for advanced undergraduate and graduate courses
in mathematics and engineering. Necessary prerequisites for this text
are basic calculus and linear algebra. Some elementary knowledge of
ordinary differential equations is also preferable.
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