## Advanced vector analysis for scientists and engineersVector analysis is one of the most useful branches of mathematics. It is a highly scientific field that is used in practical problems arising in engineering and applied sciences. Based on notes gathered throughout the many years of teaching vector calculus, the main purpose of the book is to illustrate the application of vector calculus to physical problems. The theory is explained elegantly and clearly and there is an abundance of solved problems to manifest the application of the theory. The beauty of this book is the richness of practical applications. There are nine chapters each of which contains ample exercises at the end. A bibliography list is also included for ready reference. The book concludes with two appendices. Appendix A contains answers to some selected exercises, and Appendix B contains some useful vector formulas at a glance.This book is suitable for a one semester course for senior undergraduates and junior graduate students in science and engineering. It is also suitable for the scientists and engineers working on practical problems. |

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### Contents

Preface | 1 |

Vector functions of one variable | 31 |

Partial derivatives of functions of several variables | 55 |

Copyright | |

9 other sections not shown

### Common terms and phrases

arbitrary arc length axes calculate Cartesian coordinates Chapter components coordinate system curl curvilinear coordinates cylindrical coordinates defined definition denote density differential divergence theorem dot product dr dr dx dy dz electromagnetic equation Evaluate Example expression field F Figure Find flow fluid flux formula given grad gradient Green's theorem heat equation Hence identity independent of path Laplace's equation level surface line integral magnitude Maxwell's equations obtain octant oriented orthogonal curvilinear coordinates osculating plane parameter partial derivatives perpendicular polar coordinates position vector potential projection quantities quaternions rate of change region respect scalar function scalar product scale factors shown in Fig smooth curve Solution space sphere x2 spherical coordinates Stokes surface integral tangent vector triple integral unit tangent unit vector variable vector analysis vector field vector function vector product volume integral wave wavenumbers zero