Fourier Series and Numerical Methods for Partial Differential Equations (PDF)

The importance of partial differential equations (PDEs) in modeling
phenomena in engineering as well as in the physical, natural, and
social sciences is well known by students and practitioners in
these fields. Striking a balance between theory and applications,
Fourier Series and Numerical Methods for Partial Differential
Equations presents an introduction to the analytical and
numerical methods that are essential for working with partial
differential equations. Combining methodologies from calculus,
introductory linear algebra, and ordinary differential equations
(ODEs), the book strengthens and extends readers' knowledge of the
power of linear spaces and linear transformations for purposes of
understanding and solving a wide range of PDEs.

The book begins with an introduction to the general terminology
and topics related to PDEs, including the notion of initial and
boundary value problems and also various solution techniques.
Subsequent chapters explore:

* The solution process for Sturm-Liouville boundary value ODE
problems and a Fourier series representation of the solution of
initial boundary value problems in PDEs

* The concept of completeness, which introduces readers to
Hilbert spaces

* The application of Laplace transforms and Duhamel's theorem to
solve time-dependent boundary conditions

* The finite element method, using finite dimensional
subspaces

* The finite analytic method with applications of the
Fourier series methodology to linear version of non-linear
PDEs

Throughout the book, the author incorporates his own
class-tested material, ensuring an accessible and easy-to-follow
presentation that helps readers connect presented objectives with
relevant applications to their own work. Maple is used throughout
to solve many exercises, and a related Web site features Maple
worksheets for readers to use when working with the book's one- and
multi-dimensional problems.

Fourier Series and Numerical Methods for Partial Differential
Equations is an ideal book for courses on applied mathematics
and partial differential equations at the upper-undergraduate and
graduate levels. It is also a reliable resource for researchers and
practitioners in the fields of mathematics, science, and
engineering who work with mathematical modeling of physical
phenomena, including diffusion and wave aspects.