## Vector and Tensor Analysis, Second EditionRevised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved. |

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### Contents

VECTOR ALGEBRA | 1 |

DIFFERENTIAL CALCULUS OF VECTOR | 75 |

DIFFERENTIAL CALCULUS OF SCALAR | 147 |

3 Directional Derivative of a Scalar Field | 154 |

INTEGRAL CALCULUS OF SCALAR | 207 |

grals of Vector Fields 4 3 Properties of Line | 235 |

Representation of Surfaces 4 7 Surface Area | 288 |

Stokes Theorem | 296 |

TENSORS IN RECTANGULAR CARTESIAN | 307 |

Cartesian Coordinate Systems 5 4 Transformation | 321 |

TENSORS IN GENERAL COORDINATES | 373 |

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acceleration algebra angle applications assume axes base basis calculate called cartesian coordinate circle closed components consider constant continuous contravariant coordinate system corresponding covariant curl F curve cylindrical defined definition denote derivative described determined differentiable direction divergence domain equal equation Example EXERCISES expression Find follows force formula geometric given gradient Hence implies integral line integral line segment magnitude matrix moving normal vector numbers oblique obtain operator origin orthogonal parameter particle plane position vector Problem properties quantities rectangular relation represented respect result rotation scalar field Show shown sides smooth Solution space speed sphere stress suppose surface tangent vector tensor theorem tion transformation unit vector vector field velocity Verify written zero ди ду дх