Tensor Analysis

The following sections are included:

• Foreword

• Preface

• Contents

The following sections are included:

• The Vector Concept Revisited

• A First Look at Tensors

• Assumed Background

• More on the Notion of a Vector

The following sections are included:

• Change of Basis

• Dual Bases

• Transformation to the Reciprocal Frame

• Transformation Between General Frames

• Covariant and Contravariant Components

• The Cross Product in Index Notation

• Closing Remarks

The following sections are included:

• Dyadic Quantities and Tensors

• Tensors from an Operator Viewpoint

• Dyadic Components Under Transformation

• More Dyadic Operations

• Properties of Second Rank Tensors

• Extending the Dyad Idea

• Tensors of the Fourth and Higher Ranks

The following sections are included:

• Vector Fields

• Differentials and the Nabla Operator

• Differentiation of a Vector Function

• Derivatives of the Frame Vectors

• Christoffel Coefficients and their Properties

• Covariant Differentiation

• Covariant Derivative of a Second Rank Tensor

• Differential Operations

• Orthogonal Coordinate Systems

• Some Formulas of Integration

• Norms on Spaces of Vectors and Tensors

The following sections are included:

• Elementary Facts from the Theory of Curves

• The Torsion of a Curve

• Serret–Frenet Equations

• Elements of the Theory of Surfaces

• The Second Fundamental Form of a Surface

• Derivation Formulas

• Implicit Representation of a Curve; Contact of Curves

• Osculating Paraboloid

• The Principal Curvatures of a Surface

• Surfaces of Revolution

• Natural Equations of a Curve

• A Word About Rigor

• Conclusion

The following sections are included:

• Appendix A Formulary

• Appendix B Hints and Answers

• Bibliography

• Index