Fourier Series and Numerical Methods for Partial Differential Equations

The importance of partial differential equations (PDEs) in modelingphenomena in engineering as well as in the physical, natural, andsocial sciences is well known by students and practitioners inthese fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial DifferentialEquations presents an introduction to the analytical andnumerical methods that are essential for working with partialdifferential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations(ODEs), the book strengthens and extends readers' knowledge of thepower of linear spaces and linear transformations for purposes ofunderstanding and solving a wide range of PDEs.
The book begins with an introduction to the general terminologyand topics related to PDEs, including the notion of initial andboundary value problems and also various solution techniques. Subsequent chapters explore:
* The solution process for Sturm-Liouville boundary value ODEproblems and a Fourier series representation of the solution ofinitial boundary value problems in PDEs
* The concept of completeness, which introduces readers toHilbert spaces
* The application of Laplace transforms and Duhamel's theorem tosolve time-dependent boundary conditions
* The finite element method, using finite dimensionalsubspaces
* The finite analytic method with applications of theFourier series methodology to linear version of non-linearPDEs
Throughout the book, the author incorporates his ownclass-tested material, ensuring an accessible and easy-to-followpresentation that helps readers connect presented objectives withrelevant applications to their own work. Maple is used throughoutto solve many exercises, and a related Web site features Mapleworksheets for readers to use when working with the book's one- andmulti-dimensional problems.
Fourier Series and Numerical Methods for Partial DifferentialEquations is an ideal book for courses on applied mathematicsand partial differential equations at the upper-undergraduate andgraduate levels. It is also a reliable resource for researchers andpractitioners in the fields of mathematics, science, andengineering who work with mathematical modeling of physicalphenomena, including diffusion and wave aspects.