## Advanced calculus for applicationsThe text provides advanced undergraduates with the necessary background in advanced calculus topics, providing the foundation for partial differential equations and analysis. Readers of this text should be well-prepared to study from graduate-level texts and publications of similar level. Ordinary Differential Equations; The Laplace Transform; Numerical Methods for Solving Ordinary Differential Equations; Series Solutions of Differential Equations: Special Functions; Boundary-Value Problems and Characteristic-Function Representations; Vector Analysis; Topics in Higher-Dimensional Calculus; Partial Differential Equations; Solutions of Partial Differential Equations of Mathematical Physics; Functions of a Complex Variable; Applications of Analytic Function Theory For all readers interested in advanced calculus. |

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User Review - Maureen - GoodreadsCould use more explanation and examples, but really grew on me. Read full review

### Contents

Ordinary Differential Equations | 1 |

The Laplace Transform | 53 |

3 | 77 |

Copyright | |

11 other sections not shown

### Common terms and phrases

analytic function angle approximation assumed Bessel functions branch points calculate Chapter characteristic functions circle coefficients complex potential considered contour converges coordinates corresponding cosh defined denote determined direction divergence theorem dx dy end conditions equivalent evaluate Example exists expansion expression Figure flow fluid follows formula Fourier function f(x given Green's function independent infinite interval involving Laplace transform Laplace's equation limit linear mapping method normal notation Notice odd function partial derivatives partial differential equation particular solution piecewise poles polynomial positive integer prescribed real and imaginary real axis region regular singular point relation replaced residue calculus respect result of Problem right-hand member satisfy the equation Section single-valued singular point sinh specified Suppose Taylor series tend to zero theorem tion unit upper half upper half-plane valid values vanish variable vector velocity Verify whereas write xy plane