Postmodern Analysis
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented here from what has been called "...
Main Author: | |
---|---|
Format: | eBook |
Language: | English |
Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003, 2003
|
Edition: | 2nd ed. 2003 |
Series: | Universitext
|
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Calculus for Functions of One Variable
- 0. Prerequisites
- 1. Limits and Continuity of Functions
- 2. Differentiability
- 3. Characteristic Properties of Differentiable Functions. Differential Equations
- 4. The Banach Fixed Point Theorem. The Concept of Banach Space
- 5. Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
- 6. Integrals and Ordinary Differential Equations
- II. Topological Concepts
- 7. Metric Spaces: Continuity, Topological Notions, Compact Sets
- III. Calculus in Euclidean and Banach Spaces
- 8. Differentiation in Banach Spaces
- 9. Differential Calculus in ?d
- 10. The Implicit Function Theorem. Applications
- 11. Curves in ?d. Systems of ODEs
- IV. The Lebesgue Integral
- 12. Preparations. Semicontinuous Functions
- 13. The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets
- 14. Lebesgue Integrable Functions and Sets
- 15. Null Functions and Null Sets. The Theorem of Fubini
- 16. The Convergence Theorems of Lebesgue Integration Theory
- 17. Measurable Functions and Sets. Jensen’s Inequality. The Theorem of Egorov
- 18. The Transformation Formula
- V. Lp and Sobolev Spaces
- 19. The Lp-Spaces
- 20. Integration by Parts. Weak Derivatives. Sobolev Spaces
- VI. Introduction to the Calculus of Variations and Elliptic Partial Differential Equations
- 21. Hilbert Spaces. Weak Convergence
- 22. Variational Principles and Partial Differential Equations
- 23. Regularity of Weak Solutions
- 24. The Maximum Principle
- 25. The Eigenvalue Problem for the Laplace Operator
- Index of Notation