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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
J G Papastavridis |

ISBN: | 0849385148 9780849385148 |

OCLC Number: | 39313632 |

Description: | xlvii, 386 pages : illustrations ; 24 cm. |

Contents: | Tensors and Geometry -- Tensors and Physics -- Tensors and Mechanics -- Exterior Forms (Cartan Calculus) -- Some Algebra -- Symmetry and Antisymmetry -- The Kronecker Delta -- The Levi-Civita Permutation Symbols -- The Generalized Kronecker Delta -- The Generalized Permutation Symbols -- Linear Equations, Cramer's Rule -- Functional Determinants (Jacobians) -- Derivatives of Determinants -- Some Geometry -- Primitive Concepts -- Set -- Group (G) -- Space -- Algebraic Definition -- Coordinate System(s) (CS) -- Manifold -- Coordinate Transformation(s) (CT) -- Systems of Coordinates vs. Frames of Reference -- Successive CT, Group Property -- Admissible CT -- Invariance -- Entity, or Object, Invariance -- Form Invariance -- Manifold Orientation -- Tensor Calculus (TC) -- Subspaces in a Manifold; Curves, Surfaces, etc. -- Special Cases -- Tensor Algebra -- Introduction: Affine and Euclidean, or Metric, Vector Spaces -- Vectors -- 0. Sum -- 0'. Product with a Scalar -- 0". Scalar, or Dot, Product -- Affine and Euclidean Point Spaces -- Linear Independence, Dimension and Basis -- Local Basis, or Frame -- Vector Subspace of an X[subscript n] -- Complementary Vector Subspaces -- Vector Algebra in a Euclidean Vector Space -- Dot Product -- Covariant and Contravariant Components of a Vector -- Dual of (or to) a Basis -- Change of Basis -- Introduction to Coordinate Transformations--Affine/Rectilinear Coordinates -- General Curvilinear (Nonlinear) Coordinate Transformations (CT) -- Curvilinear Coordinates and Their Differentials. |

Series Title: | Library of engineering mathematics. |

Responsibility: | John G. Papastavridis. |

More information: |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"This is a deep and complete workin view of the fact that very few books in tensor analysis have appeared recently, the present monograph is one of the most up to datehighly recommended" -L.Y. Bahar in Applied Mechanics Review, September 1999 "The book is very carefully written and published, it should find many readers and young scientists who want to follow the beautiful Analytical Dynamics in research and teaching." -Professor Peter MaiBer Applied Mechanics Review, September 1999 "The material covered in the book is certainly of a high interest in spite of the long tradition accumulated in the past and a considerable number of textbooks published... the book is intended to be a concise introductory tool to theoretical dynamics and aims to provide the reader with a strong background on the geometrical concepts supporting the formulation of the general equations of motion of constrained mechanical systems... Papastavridis achieves his purpose in handing down a coherent and understandable presentation inclusive of some solved examples and problems... The volume represents a valuable contribution to the dissemination of knowledge in the field of theoretical mechanics and may be recommended for graduate students and researchers in engineering, physics, and applied mathematics." -Meccanica, vol. 35, #5, 2001 Read more...

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