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Applicable Differential Geometry

Applicable Differential Geometry

$139.00 (P)

Part of London Mathematical Society Lecture Note Series

  • Date Published: April 1987
  • availability: Available
  • format: Paperback
  • isbn: 9780521231909

$ 139.00 (P)
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  • This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half. Analysis is included not for its own sake, but only where it illuminates geometrical ideas. The style is informal and clear yet rigorous; each chapter ends with a summary of important concepts and results. In addition there are over 650 exercises, making this a book which is valuable as a text for advanced undergraduate and postgraduate students.

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    Product details

    • Date Published: April 1987
    • format: Paperback
    • isbn: 9780521231909
    • length: 404 pages
    • dimensions: 229 x 152 x 23 mm
    • weight: 0.59kg
    • availability: Available
  • Table of Contents

    The background: vector calculus
    1. Affine spaces
    2. Curves, functions and derivatives
    3. Vector fields and flows
    4. Volumes and subspaces: exterior algebra
    5. Calculus of forms
    6. Frobenius's theorem
    7. Metrics on affine spaces
    8. Isometrics
    9. Geometry of surfaces
    10. Manifolds
    11. Connections
    12. Lie groups
    13. The tangent and cotangent bundles
    14. Fibre bundles
    15. Connections revisited.

  • Authors

    M. Crampin, The Open University, Milton Keynes

    F. A. E. Pirani, University of London

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