Absolute Analysis
The first edition of this book, published in German, came into being as the result of lectures which the authors held over a period of several years since 1953 at the Universities of Helsinki and Zurich. The Introduction, which follows, provides information on what moti vated our presentation of an...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973, 1973
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| Edition: | 1st ed. 1973 |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Linear Algebra
- § 1. The Linear Space with Real Multiplier Domain
- § 2. Finite Dimensional Linear Spaces
- § 3. Linear Mappings
- § 4. Bilinear and Quadratic Functions
- § 5. Multilinear Functions
- § 6. Metrization of Affine Spaces
- II. Differential Calculus
- § 1. Derivatives and Differentials
- § 2. Taylor’s Formula
- § 3. Partial Differentiation
- § 4. Implicit Functions
- III. Integral Calculus
- § 1. The Affine Integral
- § 2. Theorem of Stokes
- § 3. Applications of Stokes’s Theorem
- IV. Differential Equations
- § 1. Normal Systems
- § 2. The General Differential Equation of First Order
- § 3. The Linear Differential Equation of Order One
- V. Theory of Curves and Surfaces
- § 1. Regular Curves and Surfaces
- § 2. Curve Theory
- § 3. Surface Theory
- § 4. Vectors and Tensors
- § 5 Integration of the Derivative Formulas
- § 6. Theorema Egregium
- § 7. Parallel Translation
- § 8. The Gauss-Bonnet Theorem
- VI. Riemannian Geometry
- § 1. Affine Differential Geometry
- § 2. Riemannian Geometry