## Fourier Series and Boundary Value Problems |

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### Contents

THE METHOD OF SEPARATION OF VARIABLES | 23 |

ORTHOGONAL SETS OF FUNCTIONS | 46 |

FOURIER SERIES | 78 |

Copyright | |

7 other sections not shown

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### Common terms and phrases

assume axis Bessel functions Bessel's equation Bibliography boundary conditions boundary value problem coefficients continuous functions converges uniformly corresponding cosine series cylinder defined denote eigenfunctions eigenvalues exist finite number follows Fourier cosine series Fourier integral Fourier series Fourier sine series fundamental interval harmonic function heat equation Hence homogeneous equations improper integral inner product insulated integral formula integrand interval 0,c interval a,b Jn(x Laplace's equation Legendre polynomials Lemma linear combination Note nx dx obtained one-sided derivatives orthonormal set partial differential equations period 2n periodic extension piecewise continuous plane Pn(x positive constant positive integer positive number positive roots represents respect satisfies the conditions separation of variables series converges series representation sinh slab Sm(x solve steady temperatures string Sturm-Liouville problem surface temperature zero Theorem tion transform uniform convergence vectors Verify wave equation write written