Introduction to Vectors and Tensors Vol 2 (Bowen 246). - Index of
Introduction to Vectors and Tensors Vol 2 (Bowen 246). - Index of Introduction to Vectors and Tensors Vol 2 (Bowen 246). - Index of
vi CONTENTS OF VOLUME 2 Section 61. Surface Area, Minimal Surface………........................ 454 Section 62. Surfaces in a Three-Dimensional Euclidean Manifold. 457 CHAPTER 12. Elements of Classical Continuous Groups Section 63. The General Linear Group and Its Subgroups……….. 463 Section 64. The Parallelism of Cartan……………………………. 469 Section 65. One-Parameter Groups and the Exponential Map…… 476 Section 66. Subgroups and Subalgebras…………………………. 482 Section 67. Maximal Abelian Subgroups and Subalgebras……… 486 CHAPTER 13. Integration of Fields on Euclidean Manifolds, Hypersurfaces, and Continuous Groups Section 68. Arc Length, Surface Area, and Volume……………... 491 Section 69. Integration of Vector Fields and Tensor Fields……… 499 Section 70. Integration of Differential Forms……………………. 503 Section 71. Generalized Stokes’ Theorem……………………….. 507 Section 72. Invariant Integrals on Continuous Groups…………... 515 INDEX………………………………………………………………………. x
______________________________________________________________________________ CONTENTS Vol. 1 Linear and Multilinear Algebra PART 1 BASIC MATHEMATICS Selected Readings for Part I………………………………………………………… 2 CHAPTER 0 Elementary Matrix Theory…………………………………………. 3 CHAPTER 1 Sets, Relations, and Functions……………………………………… 13 Section 1. Sets and Set Algebra………………………………………... 13 Section 2. Ordered Pairs" Cartesian Products" and Relations…………. 16 Section 3. Functions……………………………………………………. 18 CHAPTER 2 Groups, Rings and Fields…………………………………………… 23 Section 4. The Axioms for a Group……………………………………. 23 Section 5. Properties of a Group……………………………………….. 26 Section 6. Group Homomorphisms…………………………………….. 29 Section 7. Rings and Fields…………………………………………….. 33 PART I1 VECTOR AND TENSOR ALGEBRA Selected Readings for Part II………………………………………………………… 40 CHAPTER 3 Vector Spaces……………………………………………………….. 41 Section 8. The Axioms for a Vector Space…………………………….. 41 Section 9. Linear Independence, Dimension and Basis…………….….. 46 Section 10. Intersection, Sum and Direct Sum of Subspaces……………. 55 Section 11. Factor Spaces………………………………………………... 59 Section 12. Inner Product Spaces………………………..………………. 62 Section 13. Orthogonal Bases and Orthogonal Compliments…………… 69 Section 14. Reciprocal Basis and Change of Basis……………………… 75 CHAPTER 4. Linear Transformations……………………………………………… 85 Section 15. Definition of a Linear Transformation………………………. 85 Section 16. Sums and Products of Linear Transformations……………… 93
- Page 1: INTRODUCTION TO VECTORS AND TENSORS
- Page 5: ___________________________________
- Page 9 and 10: ___________________________________
- Page 11 and 12: ___________________________________
- Page 13 and 14: Sec. 43 • Euclidean Point Spaces
- Page 15 and 16: Sec. 43 • Euclidean Point Spaces
- Page 17 and 18: Sec. 43 • Euclidean Point Spaces
- Page 19 and 20: Sec. 43 • Euclidean Point Spaces
- Page 21 and 22: Sec. 44 • Coordinate Systems 307
- Page 23 and 24: Sec. 44 • Coordinate Systems 309
- Page 25 and 26: Sec. 44 • Coordinate Systems 311
- Page 27 and 28: Sec. 44 • Coordinate Systems 313
- Page 29 and 30: Sec. 44 • Coordinate Systems 315
- Page 31 and 32: Sec. 44 • Coordinate Systems 317
- Page 33 and 34: Sec. 44 • Coordinate Systems 319
- Page 35 and 36: Sec. 44 • Coordinate Systems 321
- Page 37 and 38: Sec. 44 • Coordinate Systems 323
- Page 39 and 40: Sec. 45 • Transformation Rules 32
- Page 41 and 42: Sec. 45 • Transformation Rules 32
- Page 43 and 44: Sec. 45 • Transformation Rules 32
- Page 45 and 46: Sec. 45 • Transformation Rules 33
- Page 47 and 48: Sec. 46 • Anholonomic and Physica
- Page 49 and 50: Sec. 46 • Anholonomic and Physica
- Page 51 and 52: Sec. 46 • Anholonomic and Physica
- Page 53 and 54: Sec. 47 • Christoffel Symbols, Co
- Page 55 and 56: Sec. 47 • Christoffel Symbols, Co
vi CONTENTS OF VOLUME 2<br />
Section 61. Surface Area, Minimal Surface………........................ 454<br />
Section 62. Surfaces in a Three-Dimensional Euclidean Manifold. 457<br />
CHAPTER 12.<br />
Elements <strong>of</strong> Classical Continuous Groups<br />
Section 63. The General Linear Group <strong>and</strong> Its Subgroups……….. 463<br />
Section 64. The Parallelism <strong>of</strong> Cartan……………………………. 469<br />
Section 65. One-Parameter Groups <strong>and</strong> the Exponential Map…… 476<br />
Section 66. Subgroups <strong>and</strong> Subalgebras…………………………. 482<br />
Section 67. Maximal Abelian Subgroups <strong>and</strong> Subalgebras……… 486<br />
CHAPTER 13.<br />
Integration <strong>of</strong> Fields on Euclidean Manifolds, Hypersurfaces, <strong>and</strong><br />
Continuous Groups<br />
Section 68. Arc Length, Surface Area, <strong>and</strong> <strong>Vol</strong>ume……………... 491<br />
Section 69. Integration <strong>of</strong> Vec<strong>to</strong>r Fields <strong>and</strong> Tensor Fields……… 499<br />
Section 70. Integration <strong>of</strong> Differential Forms……………………. 503<br />
Section 71. Generalized S<strong>to</strong>kes’ Theorem……………………….. 507<br />
Section 72. Invariant Integrals on Continuous Groups…………... 515<br />
INDEX……………………………………………………………………….<br />
x
Change language