Fourier analysis and boundary value problems 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. Index 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. Key Features * Topics are covered from a historical perspective with biographical information on key contributors to the field * The text contains more than 500 exercises * Includes practical applications of the equations to problems in both engineering and physics