## Elementary Partial Differential Equations |

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### Contents

Introduction | 1 |

Linear equations with constant coefficients in | 18 |

The heat equation and related equations | 29 |

Copyright | |

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### Common terms and phrases

absolutely integrable applied arbitrary assume becomes boundary conditions bounded calculation called Chapter coefficients complex consider constant convergence corresponding defined derivatives determined differential equation discussion distribution domain dx dy eigenfunctions eigenvalue problem energy equilibrium establish example EXERCISES exist expansion fact finite fixed force formula Fourier series function given heat hence holds homogeneous independent infinite initial initial-boundary value problem integral interval kind length limit linear maximum method multiplicity obtain operator ordinary differential orthogonal partial differential particular periodic physical piecewise continuous positive problem D.E. proof prove representation require respect result roots satisfies Show smooth solution Solve statement string Substituting suppose temperature theorem tion transform uniform uniqueness variables verify vibrations wave equation zero λφ ди