Fourier Series and Boundary Value Problems |
Contents
Preface | 1 |
SUPERPOSITION OF SOLUTIONS | 23 |
ORTHOGONAL SETS OF FUNCTIONS | 49 |
Copyright | |
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a₁ axis b₂ Bessel's equation boundary conditions boundary value problem bounded C₁ C₂ coefficients constant continuous function converges to f(x converges uniformly cosine series cylinder defined denote domain eigenfunctions eigenvalues exist f is continuous f(xo finite number follows Fourier cosine series Fourier series Fourier sine series Fourier theorem function f heat equation Hence homogeneous conditions infinite inner product insulated integrand interior interval 0,c interval a,b Jn(x Jo(x Laplace's equation Legendre's linear combination Note nx dx one-sided derivatives orthonormal set partial differential equations periodic extension periodic function plane polynomials positive number positive roots represents respect satisfies the conditions sectionally continuous function separation of variables series converges sinh string Sturm-Liouville problem surface temperature zero tion u₁ uniform convergence vector write written ди ппх