2013

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Authors:

ISBN: 978-1-4614-7866-9 (Print) 978-1-4614-7867-6 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiii

  2. No Access

    Book Chapter

    Pages 1-7

    Why Tensor Calculus?

  3. Tensors in Euclidean Spaces

    1. Front Matter

      Pages 9-9

    2. No Access

      Book Chapter

      Pages 11-20

      Rules of the Game

    3. No Access

      Book Chapter

      Pages 21-34

      Coordinate Systems and the Role of Tensor Calculus

    4. No Access

      Book Chapter

      Pages 35-51

      Change of Coordinates

    5. No Access

      Book Chapter

      Pages 53-73

      The Tensor Description of Euclidean Spaces

    6. No Access

      Book Chapter

      Pages 75-92

      The Tensor Property

    7. No Access

      Book Chapter

      Pages 93-104

      Elements of Linear Algebra in Tensor Notation

    8. No Access

      Book Chapter

      Pages 105-132

      Covariant Differentiation

    9. No Access

      Book Chapter

      Pages 133-157

      Determinants and the Levi-Civita Symbol

  4. Tensors on Surfaces

    1. Front Matter

      Pages 159-159

    2. No Access

      Book Chapter

      Pages 161-184

      The Tensor Description of Embedded Surfaces

    3. No Access

      Book Chapter

      Pages 185-197

      The Covariant Surface Derivative

    4. No Access

      Book Chapter

      Pages 199-213

      Curvature

    5. No Access

      Book Chapter

      Pages 215-233

      Embedded Curves

    6. No Access

      Book Chapter

      Pages 235-246

      Integration and Gauss’s Theorem

  5. The Calculus of Moving Surfaces

    1. Front Matter

      Pages 247-247

    2. No Access

      Book Chapter

      Pages 249-265

      The Foundations of the Calculus of Moving Surfaces

    3. No Access

      Book Chapter

      Pages 267-277

      Extension to Arbitrary Tensors

    4. No Access

      Book Chapter

      Pages 279-295

      Applications of the Calculus of Moving Surfaces

  6. Back Matter

    Pages 297-302