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VIA VECTOR TO TENSOR【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

W·G·BICKLEY 著
出版社： THE ENGLISH UNIVERSITIES PRESS LTD
ISBN：
出版时间：未知
标注页数：152页
文件大小：5MB
文件页数：165页
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图书目录

PART Ⅰ-VECTORS1

CHAPTER 2 VECTOR ALGEBRA3

What is a vector?3

Scalars and vectors3

Some other vector quantities4

Components and resolved parts6

Vector addition and subtraction7

Unit vectors8

The scalar product9

The vector product12

Triple products14

Instructive Exercises16

CHAPTER 2 SOME APPLICATIONS TO GEOMETRY AND DYNAMICS18

Points,lines and planes18

Differentiation of vectors19

Some geometry20

Higher derivatives21

Instructive Exercises23

CHAPTER 3 VECTOR FIELDS25

Work and potential energy25

The gradient vector26

Volume and surface integrals29

Divergence30

Circuital relations33

The curl of a vector34

Instructive Exercises37

CHAPTER 4 COMBINED OPERATORS39

Null and meaningless operations39

The scalar Laplacian40

The vector Laplacian41

Representation of an arbitrary vector41

Another vector operator42

Curvilinear co-ordinates．Differential elements42

Vector formulae44

Conformal transformation44

Instructive Exercises45

PART Ⅱ-TENSORS47

CHAPTER 5 TENSORS AND THEIR TRANSFORMATION49

Introduction49

Two types of vector components50

Some notation53

Tensors of higher ranks56

Invariants57

Densities and tensor densities59

Contraction60

Instructive Exercises61

Appendix62

CHAPTER 6 COVARIANT DIFFERENTIATION63

Introduction63

Differentiation of a tensor63

Curl of a vector64

The covariant derivatives65

Covariant differentiation68

Some examples69

A further illustration72

Parallel transfer75

An example77

Instructive Exercises79

CHAPTER 7 THE METRIC TENSOR80

Introduction80

Metric tensor81

Contravariant metric tensor82

Raising and lowering indices84

Covariant vector components84

Three-index symbols85

Covariant derivatives of the metric tensor86

Instructive Exercises87

CHAPTER 8 SOME GEOMETRY89

Introduction89

Curves89

Tangent vector90

Intrinsic derivative91

Principal normal and curvature92

Binormal and the torsion93

Geodesics96

Minimal distance98

Surfaces100

Surface metric101

Curves on a surface103

Curvature of a surface106

Curvature．Curved space106

Integrability107

The Riemann-Christoffel tensor108

Gaussian or total curvature of a surface110

Normal vector of the surface110

The third fundamental differential form112

Equations of Gauss and Codazzi113

Curves on a surface116

Principal curvatures of a surface117

Instructive Exercises119

CHAPTER 9 TENSORS IN MATHEMATICAL PHYSICS121

Introduction121

Vectors121

Maxwell＇s equations125

Elasticity and fluid mechanics126

Stream function and stress function131

Instructive Exercises132

Appendix 1 Suggestions for further reading134

Appendix 2 Tensor and physical components136

Hints and Answers to the Exercises139

Index141