2. TANGENT VECTOR SPACE

Chapters in this book

1. i-vi i
2. CONTENTS vii
3. PREFACE xv
4. CHAPTER Ο. INTRODUCTION TO TENSORS
5. 1. WELL KNOWN CONCEPTS 1
6. 2. OPERATIONS ON TENSORS 19
7. CHAPTER 1. FOUNDATIONS OF DIFFERENTIAL GEOMETRY
8. 1. MANIFOLDS 25
9. 2. TANGENT VECTOR SPACE 42
10. 3. TANGENT BUNDLE, VECTOR FIELD, AND LIE ALGEBRA 59
11. 4. COTANGENT BUNDLE AND COVECTOR FIELDS 75
12. 5. TENSOR ALGEBRA AND TENSOR FIELDS 83
13. 6. EXTERIOR DIFFERENTIAL FORMS 94
14. 7. LIE DERIVATIVE, LIE GROUP, AND LIE ALGEBRA 122
15. 8. INTEGRATION OF FORMS 173
16. 9. RIEMANNIAN GEOMETRY 192
17. EXERCISES 234
18. CHAPTER 2. SYMPLECTIC GEOMETRY
19. 1. PRELIMINARIES 253
20. 2. SYMPLECTIC GEOMETRY 258
21. CHAPTER 3. A MODERN EXPOSITION OF MECHANICS
22. 1. LAGRANGIAN MECHANICS 285
23. 2. HAMILTONIAN MECHANICS 306
24. 3. COMPARISON OF THE LAGRANGIAN AND HAMILTONIAN FORMULATIONS 334
25. 4. HAMILTON–JACOBI MECHANICS 370
26. 5. INTRODUCTION TO PERTURBATIONS 409
27. EXERCISES 460
28. CHAPTER 4. THE N-BODY PROBLEM; AN ORIGINAL METHOD FOR LARGE Ν
29. 1. N-BODY PROBLEM, EQUATIONS AND INTEGRALS 481
30. 2. THE N-BODY PROBLEM IN STATISTICAL MECHANICS 523
31. BIBLIOGRAPHY 553
32. GLOSSARY OF SYMBOLS 557
33. INDEX 563