## Introduction to partial differential equations and Hilbert space methodsEasy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course. |

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### Contents

Fourier Series and Hilbert Space | 138 |

Appendix FirstOrder Equations | 236 |

Selected Answers Hints and Solutions | 245 |

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### Common terms and phrases

approximation arbitrary assume bifurcation boundary conditions boundary value problem bounded called change of variable coefficients complete consider constant continuous convergence theorem countable derivatives differential operators Dini test Dirichlet principle Dirichlet problem discussion divergence theorem domain ft eigenfunctions eigenvalue problem elliptic energy example exists formula Fourier series Fourier transform fundamental given grad Green's function heat equation Hilbert space hyperbolic identity initial data initial value problem inner product interval inverse latter Lebesgue Lemma mathematical maximal orthonormal set maximum principle nonlinear norm obtain ordinary differential equations orthogonal parabolic partial differential equations partial sums physical plane pointwise convergence Poisson Poisson problem proof Rayleigh recall scattering Section 2.6 self-adjoint separation of variables shown sinh solution u(x solve spectrum square integrable Sturm-Liouville surface temperature theory unbounded domains uniqueness variational vector vibrating string problem wave equation zero