Advanced calculus : a differential forms approach /
| Main Author: | |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boston :
Birkhäuser,
1994.
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| Edition: | Third edition]. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- ch. 1 Constant forms
- 1.1 One-forms
- 1.2 Two-forms
- 1.3 The Evaluation of the two-forms, pullbacks
- 1.4 Three-forms
- 1.5 Summary
- ch. 2 Integrals 2.1 Non-constant forms
- 2.2 Integration
- 2.3 Definition of certain simple integrals, convergence and the cauchy criterion
- 2.4 Integrals and pullbacks
- 2.5 Independence
- 2.6 Summary, Basic properties of integrals ch. 3 Integration and differentiation
- 3.1 The Fundamental theorum of calculus
- 3.2 The Fundamental theorum of two dimensions
- 3.3 The Fundamental theorum of three dimensions
- 3.4 Summary, Stokes theorum
- ch. 4 Linear algebra
- 4.1 Introduction
- 4.2 Constant k-form on n-space
- 4.3 Matrix notation, Jacobians
- 4.4 The Implicit function theorem for Affine maps
- 4.5 Abstract vector spaces
- 4.6 Summary, Affine manifolds
- ch. 5 Differential calculus
- 5.1 The Implicit function theorem for differentiable maps
- 5.2 k-forms on n-space. Differentiable maps
- 5.3 Proofs
- 5.4 Application: Lagrange multipliers
- 5.5 Summary, Differentiable manifolds ch. 6 Integral calculus-- 6.1 Summary
- 6.2 k-dimensional volume
- 6.3 Independence of parameter and the definiton of sine
- 6.4 Manifolds-with-boundary and Stokes' theorem
- 6.5 General properties of integrals
- 6.6 Integrals as functions of S ch. 7 Practical methods of solution
- 7.1 Successive approximation
- 7.2 Solution of linear equations
- 7.3 Newton's method
- 7.4 Solution of ordinary differntial equations
- 7.5 Three global problems
- ch. 8 Applications
- 8.1 Vector calculus
- 8.2 Elementary differential equations-- 8.3 Harmonic functions and conformal coordinates
- 8.4 Functions of a complex variable
- 8.5 Integrability conditions
- 8.6 Introduction to homology theory-- 8.7 Flows-- 8.8 Applications of mathematical physics
- ch. 9 Further study of limits
- 9.1 The Real number system
- 9.2 Real functions of real variables
- 9.3 Uniform continuity and differentiability
- 9.4 Compactness
- 9.5 Other types of limits
- 9.6 Interchange of limits
- 9.7 Lebesgue integration
- 9.8 Banach spaces.