DIFFERENTIAL FORMS WITH APPLICATIONS TO THE PHYSICAL SCIENCESpdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
下载压缩包 [复制下载地址] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页

DIFFERENTIAL FORMS WITH APPLICATIONS TO THE PHYSICAL SCIENCESPDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Ⅰ．Introduction 1

1．1．Exterior Differential Forms 1

1．2．Comparison with Tensors 2

Ⅱ．Exterior algebra 5

2．1．The Space of p-vectors 5

2．2．Determinants 7

2．3．Exterior Products 8

2．4．Linear Transformations 10

2．5．Inner Product Spaces 12

2．6．Inner Products of p-vectors 14

2．7．The Star Operator 15

2．8．Problems 17

Ⅲ．The Exterior Derivative 19

3．1．Differential Forms 19

3．2．Exterior Derivative 20

3．3．Mappings 22

3．4．Change of Coordinates 25

3．5．An Example from Mechanics 26

3．6．Converse of the Poincaré Lemma 27

3．7．An Example 30

3．8．Further Remarks 30

3．9．Problems 31

Ⅳ．Applications 32

4．1．Moving Frames in E3 32

4．2．Relation between Orthogonal and Skew-symmetric Matrices 35

4．3．The 6-dimensional Frame Space 37

4．4．The Laplacian，Orthogonal Coordinates 38

4．5．Surfaces 40

4．6．Maxwell＇s Field Equations 44

4．7．Problems 48

Ⅴ．Manifolds and Integration 49

5．1．Introduction 49

5．2．Manifolds 49

5．3．Tangent Vectors 53

5．4．Differential Forms 55

5．5．Euclidean Simplices 57

5．6．Chains and Boundaries 61

6．7．Integration of Forms 63

5．8．Stokes＇ Theorem 64

5．9．Periods and De Rham＇s Theorems 66

5．10．Surfaces； Some Examples 69

5．11．Mappings of Chains 71

5．12．Problems 73

Ⅵ．Applications in Euclidean space 74

6．1．Volumes in En 74

6．2．Winding Numbers，Degree of a Mapping 77

6．3．The Hopf Invariant 79

6．4．Linking Numbers，the Gauss Integral，Ampere＇s Law 79

Ⅶ．Applications to Differential Equations 82

7．1．Potential Theory 82

7．2．The Heat Equation 90

7．3．The Frobenius Integration Theorem 92

7．4．Applications of the Frobenius Theorem 102

7．5．Systems of Ordinary Equations 106

7．6．The Third Lie Theorem 108

Ⅷ．Applications to Differential Geometry 112

8．1．Surfaces(Continued) 112

8．2．Hypersurfaces 116

8．3．Riemannian Geometry，Local Theory 127

8．4．Riemannian Geometry，Harmonic Integrals 136

8．5．Affine Connection 143

8．6．Problems 148

Ⅸ．Application to Group Theory 150

9．1．Lie Groups 150

9．2．Examples of Lie Groups 151

9．3．Matrix Groups 153

9．4．Examples of Matrix Groups 154

9．5．Bi-invariant Forms 158

9．6．Problems 161

Ⅹ．Applications to Physics 163

10．1．Phase and State Space 163

10．2．Hamiltonian Systems 165

10．3．Integral-invariants 171

10．4．Brackets 179

10．5．Contact Transformations 183

10．6．Fluid Mechanics 188

10．7．Problems 193

BIBLIOGRAPHY 197

GLOSSARY OF NOTATION 199

INDEX 201