## Elementary Differential Equations with Boundary Value ProblemsWritten in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material. |

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### Contents

Introduction | 1 |

First Order Equations | 25 |

Numerical Methods | 87 |

Copyright | |

15 other sections not shown

### Common terms and phrases

characteristic polynomial coefficients complementary equation compute defined direction field eigenvalue Euler semilinear method Euler's method EXAMPLE Figure find approximate values formula Fourier Fourier sine series Frobenius solutions function fundamental set graph implicit solution implies improved Euler method initial condition initial value problem integral curves integrating factor Laplace transform linear linearly independent method with step obtained open interval open interval containing order equation particular solution power series real number rewrite Runge-Kutta method satisfies Section 2.1 separation of variables set of solutions Show sinh solution of Ly Solve the initial step sizes h Suppose tion trajectories unique solution variables Verify Wronskian y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y yields yyy yyy yyy zero