Analysis on manifolds
Material type:
TextSeries: The advanced book programPublication details: Routledge 1991 Boca RatonDescription: xi, 366 p. Includes bibliographical reference and indexISBN: - 9781138329270
- 516.07 M8A6
| Item type | Current library | Item location | Collection | Shelving location | Call number | Status | Date due | Barcode | |
|---|---|---|---|---|---|---|---|---|---|
| Books | Vikram Sarabhai Library | Rack 28-A / Slot 1383 (0 Floor, East Wing) | Non-fiction | General Stacks | 516.07 M8A6 (Browse shelf(Opens below)) | Available | 201528 |
Table of Contents
CHAPTER 1: The Algebra and Topology of Rn
Â1. Review of Linear Algebra
Â2. Matrix Inversion and Determinants
Â3. Review of Topology in Rn
Â4. Compact Subspaces and Connected Subspaces of Rn
CHAPTER 2: Differentiation
Â5. The Derivative
Â6. Continuously Differentiable Functions
Â7. The Chain Rule
Â8. The Inverse Function Theorem
*Â9. The Implicit Function Theorem
CHAPTER 3: Integration
Â10. The Integral over a Rectangle
Â11. Existence of the Integral
Â12. Evaluation of the Integral
Â13. The Integral over a Bounded Set
Â14. Rectifiable Sets
Â15. Improper Integrals
CHAPTER 4: Change of Variables
Â16. Partitions of Unity
Â17. The Change of Variables Theorem
Â18. Diffeomorphisms in Rn
Â19. Proof of the Change of Variables Theorem
Â20. Applications of Change of Variables
CHAPTER 5: Manifolds
Â21. The Volume of a Parallelopiped
Â22. The Volume of a Parametrized-Manifold
Â23. Manifolds in Rn
Â24. The Boundary of a Manifold
Â25. Integrating a Scalar Function over a Manifold
CHAPTER 6: Differential Forms
Â26. Multilinear Algebra
Â27. Alternating Tensors
Â28. The Wedge Product
Â29. Tangent Vectors and Differential Forms
Â30. The Differential Operator
*Â31. Application to Vector and Scalar Fields
Â32. The Action of a Differentiable Map
CHAPTER 7: Stokes' Theorem
Â33. Integrating Forms over Parametrized-Manifolds
Â34. Orientable Manifolds
Â35. Integrating Forms over Oriented Manifolds
Â36. A Geometric Interpretation of Forms and Integrals
Â37. The Generalized Stokes' Theorem
Â38. Applications to Vector Analysis
CHAPTER 8: Closed Forms and Exact Forms
Â39. The Poincaré Lemma.
Â40. The deRham Groups of Punctured Euclidean Space
CHAPTER 9: Epilogueâ℗ђ℗ؤLife Outside Rn
Â41. Differentiable Manifolds and Riemannian Manifolds
BIBLIOGRAPHY
INDEX.
A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include a series of problems to reinforce concepts.
https://www.routledge.com/Analysis-On-Manifolds/Munkres/p/book/9780201315967
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