## Geometrical VectorsEvery advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition.Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided. |

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### Contents

II | 1 |

III | 2 |

IV | 4 |

V | 6 |

VI | 8 |

VII | 9 |

VIII | 10 |

IX | 11 |

XXXVI | 60 |

XXXVII | 62 |

XXXVIII | 64 |

XXXIX | 65 |

XL | 66 |

XLI | 69 |

XLII | 71 |

XLIII | 73 |

X | 13 |

XI | 15 |

XII | 16 |

XIII | 18 |

XIV | 19 |

XV | 22 |

XVI | 24 |

XVII | 26 |

XVIII | 27 |

XIX | 28 |

XX | 31 |

XXI | 32 |

XXII | 34 |

XXIII | 36 |

XXIV | 39 |

XXV | 40 |

XXVI | 42 |

XXVII | 43 |

XXVIII | 45 |

XXIX | 48 |

XXX | 49 |

XXXI | 51 |

XXXII | 52 |

XXXIII | 53 |

XXXIV | 55 |

XXXV | 57 |

### Common terms and phrases

arbitrary arrow basis vectors arrow vector arrowhead arrows and stacks axial arrow axial scalar axial sense becomes compressed computation constant construction contravariant vector density coordinate surfaces coordinate system coordinate transformations corresponding course covariant vector capacity cross product curl curlicue cylindrical coordinate system cylindrical coordinates definition differential direction displacement distortion of space divergence dot product electric field equal equation equipotential surfaces equivalent example fact factor flavor formulas geometrical grad gradient Grand Algebraization Rule intuitive Laplacian length line integral loose edges magnitude metric multiply negative obtained operations orthogonal parallel parallelogram particle perpendicular pictorial plane relation remains result scalar capacity scalar density scalar field sheaf basis sheaf field sheaves simply specified spherical coordinates stack basis vectors stack field stack sheets tensor analysis terms of components three-dimensional three-dimensional space topologically invariant triple scalar product type of vector underlying Cartesian system unit cell universal right-hand rule volume zero

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