Fourier Series and Boundary Value Problems
An introductory treatment of Fourier series and their applications to boundary value problems in partial equations that arise in engineering and physics. This revision incorporates up-to-date mathematics. Many sections have been rewritten to improve the motivation of the theory, and numerous illustrations and exercises have been added throughout the book.
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The Fourier Method
Boundary Value Problems
6 other sections not shown
apply assume axis Bibliography boundary conditions boundary value problem bounded interval Chap coefficients continuous functions corollary in Sec cosine series cylinder defined denote derive the expression eigenfunctions eigenvalues finite number follows Fourier cosine series Fourier series Fourier sine series function f(x fundamental interval heat equation Hence homogeneous conditions insulated integral formula Laplace's equation lemma linear combination mathematical nirx nonhomogeneous nonzero normalized eigenfunctions Note nxdx obtained one-sided limits orthogonal orthonormal set partial differential equation periodic extension piecewise continuous piecewise smooth polynomials positive constant positive number positive roots respect rnrx satisfies the conditions separation of variables sinh slab sN(x solution solve space steady temperatures string Sturm-Liouville problem substitution Suppose surface temperature problem temperature zero tends to infinity tends to zero theorem in Sec uniform convergence uniformly valid verify wave equation write written xy plane