Differential Forms A Heuristic Introduction
A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an apparatus of topology and algebra which is heavy for beginning un...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1977, 1977
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| Edition: | 1st ed. 1977 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Partial Differentiation
- 1.1 Partial Derivatives
- 1.2 Differentiability, Chain Rule
- 1.3 Taylor’s Theorem
- 2 Differential Forms
- 2.1 Line Integrals
- 2.2 One Forms
- 2.3 Wedge Product
- 2.4 Change of Coordinates
- 3 Integration in Higher Dimensions
- 3.1 Jacobians
- 3.2 Implicit Function Theorem
- 3.3 Manifolds
- 3.4 Integration on Manifolds
- 4 Exterior Differentiation
- 4.2 Exterior Derivative
- 4.2 Fundamental Theorem of Calculus
- 4.3 Closed Forms
- 4.4 Exact Forms
- 5 Vector Operations in ?3
- 5.1 Nabla
- 5.2 Higher Derivatives
- 5.3 Integral Formulae
- 6 Extremals
- 6.1 Generic Extremals
- 6.2 Extremals with Constraints
- 7 Integral Geometry
- 7.1 Measure of Points and Lines
- 7.2 Kinematic Measure
- 7.3 Formulae of Poincaré and Blaschke
- 1. The Volume Element on a Manifold
- 2. The Algebra of Forms
- 3. A Remark on Curl Curl