## Differential Equations with Boundary-Value ProblemsDIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 7th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |

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### Contents

INTRODUCTION TO DIFFERENTIAL EQUATIONS | 1 |

FIRSTORDER DIFFERENTIAL EQUATIONS | 34 |

MODELING WITH FIRSTORDER DIFFERENTIAL EQUATIONS | 82 |

HIGHERORDER DIFFERENTIAL EQUATIONS | 117 |

MODELING WITH HIGHERORDER DIFFERENTIAL EQUATIONS | 181 |

SERIES SOLUTIONS OF LINEAR EQUATIONS | 219 |

THE LAPLACE TRANSFORM | 255 |

SYSTEMS OF LINEAR FIRSTORDER DIFFERENTIAL EQUATIONS | 303 |

BOUNDARYVALUE PROBLEMS IN RECTANGULAR COORDINATES | 432 |

BOUNDARYVALUE PROBLEMS IN OTHER COORDINATE SYSTEMS | 471 |

INTEGRAL TRANSFORMS | 488 |

NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS | 511 |

GAMMA FUNCTION | 527 |

MATRICES | 529 |

LAPLACE TRANSFORMS | 547 |

ANSWERS FOR SELECTED ODDNUMBERED PROBLEMS | 551 |

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Answers to selected approximate autonomous system boundary conditions boundary-value problem Cauchy-Euler equation constant converges cosh critical point defined determine dx dt dy dt dy dx dydx eigenvalues eigenvector equa equilibrium position Euler’s method Example Exercises explicit solution family of solutions first-order differential equation Fourier series function given differential equation Graph for Problem heat equation homogeneous initial conditions initial-value problem integral interval Laplace transform linear system linearly independent mass matrix motion nonhomogeneous nonlinear numerical solver obtain odd function odd-numbered problems begin orthogonal partial differential equation particular solution plane autonomous system polynomial power series regular singular point REVIEW MATERIAL RK4 method Section selected odd-numbered problems separation of variables series solution shown in Figure singular point sinh solution curve solve the given spring Sturm-Liouville problem superposition principle tank Theorem tion values variables vector velocity zero