## Vector Analysis and Cartesian Tensors, Third editionThis is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book. |

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### Contents

Scalar and vector algebra | 21 |

Vector functions of a real variable Differential geometry | 55 |

Scalar and vector fields | 89 |

Line surface and volume integrals | 147 |

Integral theorems | 195 |

Applications in potential theory | 225 |

### Common terms and phrases

a x b axes Ox axes Ox'y'z axes Oxyz axis cartesian tensor closed region Consider continuously differentiable coordinate axes coordinate system curvilinear coordinates cylindrical polar coordinates defined definition denote direction cosines div F divergence theorem double integral eigenvalues Evaluate example EXERCISES expressed F.dr field F fixed follows geometrical given grad Q Hence isotropic isotropic function isotropic tensor Laplace's equation line integral magnitude notation origin orthogonal orthonormality parallel parametric equation partial derivatives perpendicular plane Poisson's equation position vector proof prove rectangular cartesian coordinate region 2ft region V bounded relative respectively result right-hand rotation satisfied scalar field scalar invariant scalar product second order tensor Show simple closed curve simple closed surface Solution sphere spherical polar coordinates steepest descent Stokes's theorem suffixes unit normal unit tangent unit vector v-axis vector analysis vector field vector product verify vv-plane z-axis zero