## A course in ordinary and partial differential equations |

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### Contents

Elementary HigherOrder Differential Equations | 14 |

Existence Theorems | 26 |

Singular Solutions | 50 |

Copyright | |

20 other sections not shown

### Common terms and phrases

analytic applied arbitrary assume asymptotic boundary conditions bounded canonical form Cauchy problem Cauchy sequence Consider the equation constant coefficients continuous function Corollary critical point curve deduce defined Definition denote derivatives Dirichlet problem dx dy eigenfunctions eigenvalues elliptic operator Example Exercise exists Find finite fixed Fourier transform function f(x fundamental solution given Green's function Green's identity harmonic hence Hilbert space Hint homogeneous equation hyperbolic implies independent solutions independent variables inequality initial conditions integral interval Lemma linear equations linear system matrix method neighborhood nonhomogeneous norm obtain origin partial differential equations particular solution Proof Prove region regular singular point relation respect result scalar second-order Section Show solution u(x Solve sphere stable substitution surface tempered distribution Theorem 17 tion trajectories trivial solution unique solution vector Verify wave equation zeros