Vector Analysis
Classical vector analysis deals with vector fields; the gradient, divergence, and curl operators; line, surface, and volume integrals; and the integral theorems of Gauss, Stokes, and Green. Modern vector analysis distills these into the Cartan calculus and a general form of Stokes' theorem. Thi...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | Undergraduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Differentiable Manifolds
- 2 The Tangent Space
- 3 Differential Forms
- 4 The Concept of Orientation
- 5 Integration on Manifolds
- 6 Manifolds-with-Boundary
- 7 The Intuitive Meaning of Stokes’s Theorem
- 8 The Wedge Product and the Definition of the Cartan Derivative
- 9 Stokes’s Theorem
- 10 Classical Vector Analysis
- 11 De Rham Cohomology
- 12 Differential Forms on Riemannian Manifolds
- 13 Calculations in Coordinates
- 14 Answers to the Test Questions