Fourier Analysis and Boundary Value Problems

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.

A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

Topics are covered from a historical perspective with biographical information on key contributors to the fieldThe text contains more than 500 exercisesIncludes practical applications of the equations to problems in both engineering and physics

A Heated Discussion
Fourier Series
Return to the Heated Bar
Generalized Fourier Series
The Wave Equation
Orthogonal Systems
Fourier Transforms
Laplace Transforms
Boundary Value Problems in Higher Dimensions
Boundary Value Problems with Circular Symmetry
Boundary Value Problems with Spherical Symmetry
Uniform Convergence
Improper Integrals
Tables of Fourier and Laplace Transforms
Historical Bibliography