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书名：	Tensor Analysis
作者：	Lebedev, Leonid P.; Cloud, Michael J.
出版时间：	2003-01-01
ISBN：	9789812383600(P-ISBN) ，9789812564467(O-ISBN)
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书目详情：

Foreword Preface Contents Chapter 1 Preliminaries 1.1 The Vector Concept Revisited 1.2 A First Look at Tensors 1.3 Assumed Background 1.4 More on the Notion of a Vector Chapter 2 Transformations and Vectors 2.1 Change of Basis 2.2 Dual Bases 2.3 Transformation to the Reciprocal Frame 2.4 Transformation Between General Frames 2.5 Covariant and Contravariant Components 2.6 The Cross Product in Index Notation 2.7 Closing Remarks Chapter 3 Tensors 3.1 Dyadic Quantities and Tensors 3.2 Tensors from an Operator Viewpoint 3.3 Dyadic Components Under Transformation 3.4 More Dyadic Operations 3.5 Properties of Second Rank Tensors The tensor transpose Tensors raised to powers Symmetric and antisymmetric tensors Eigenvalues and eigenvectors The Cayley-Hamilton theorem Tensors of rotation Polar decomposition Isotropic tensors and isotropic scalar functions Deviator and ball tensor representation 3.6 Extending the Dyad Idea 3.7 Tensors of the Fourth and Higher Ranks Chapter 4 Tensor Fields 4.1 Vector Fields 4.2 Differentials and the Nabla Operator 4.3 Differentiation of a Vector Function 4.4 Derivatives of the Frame Vectors 4.5 Christoffel Coefficients and their Properties 4.6 Covariant Differentiation 4.7 Covariant Derivative of a Second Rank Tensor 4.8 Differential Operations 4.9 Orthogonal Coordinate Systems 4.10 Some Formulas of Integration 4.11 Norms on Spaces of Vectors and Tensors Normed spaces Chapter 5 Elements of Differential Geometry 5.1 Elementary Facts from the Theory of Curves Curvature The moving trihedron Curves in the plane 5.2 The Torsion of a Curve 5.3 Serret–Frenet Equations 5.4 Elements of the Theory of Surfaces The first fundamental form Geodesics 5.5 The Second Fundamental Form of a Surface The normal curvature of the surface 5.6 Derivation Formulas Some useful formulas 5.7 Implicit Representation of a Curve; Contact of Curves Contact of curves Contact of a curve with a circle; evolutes Contact of nth order between a curve and a surface 5.8 Osculating Paraboloid 5.9 The Principal Curvatures of a Surface 5.10 Surfaces of Revolution 5.11 Natural Equations of a Curve 5.12 A Word About Rigor 5.13 Conclusion Appendix A Formulary Chapter 2 Reciprocal dual) basis Frame transformation Miscellaneous Chapter 3 Dyad product Tensors from operator viewpoint Dyadic components under transformation More dyadic operations Second rank tensor topics Chapter 4 Vector fields Differentials and the nabla operator Differentiation of a vector function Covariant differentiation of second-rank tensor Differential operations Orthogonal coordinate systems Integration formulas Chapter 5 Elementary theory of curves Serret-Frenet equations Theory of surfaces Appendix B Hints and Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Bibliography Index

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