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| Preface Ⅰ VECTORS, BASES AND ORTHOGONAL TRANSFOR-MATIONS 1.1 Introduction 1.2 The geometrical theory of vectors 1.3 Bases 1.4 The summation convention 1.5 The components of a vector 1.6 Transformations of base 1.7 Properties of the transformation matrix T 1.8 The orthogonal group 1.9 Examples Ⅱ THE DEFINITION OF A TENSOR 2.1 Introduction 2.2 Geometrical examples of multilinear functions of direction 2.3 Examples of multilinear functions of direction in rigid dynamics 2.4 The stress tensor in continuum dynamics 2.5 Formal definition of a tensor 2.6 The angular velocity tensor Ⅲ THE ALGEBRA OF TENSORS 3.1 Introduction 3.2 Addition and scalar multiplication 3.3 Outer multiplication 3.4 Spherical means of tensors and contraction 3.5 Symmetry and antisymmetry 3.6 Antisymmetric tensors of rank 2 3.7 Products of vectors 3.8 The Chapman-Cowling notation Ⅳ THE CALCULUS OF TENSORS 4.1 Introduction 4.2 The differentiation of tensors 4.3 Derived tensors 4.4 The strain tensor 4.5 The rate of strain tensor 4.6 The momentum equations for a continuous medium Ⅴ THE STRUCTURE OF TENSORS 5.1 Introduction 5.2 Projection operators 5.3 Definition of eigenvalues and eigenvectors 5.4 Existence of eigenvalues and eigenvectors 5.5 The secular equation Ⅴ ISOTROPIC TENSORS 6.1 Introduction 6.2 Definition of isotropic tensors 6.3 Isotropic tensors in two dimensions 6.4 Isotropic tensors of rank 2 in three dimensions 6.5 Isotropic tensors of rank 3 in three dimensions 6.6 Isotropic tensors of rank 4 in three dimensions 6.7 The stress-strain relations for an isotropic elastic medium 6.8 The constitutive equations for a viscous fluid Ⅶ SPINORS 7.1 Introduction 7.2 Isotropic vectors 7.3 The isotropic parameter 7.4 Spinors 7.5 Spinors and vectors 7.6 The Clifford algebra 7.7 The inner automorphisms of the Clifford algebra 7.8 The spinor manifold Ⅷ TENSORS IN ORTOGONAL CURVILINEAR INDEX |
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