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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 "...

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Bibliographic Details
Main Author: Jost, Jürgen
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2003, 2003
Edition:2nd ed. 2003
Series:Universitext
Subjects:
Mathematical Analysis
Analysis
Partial Differential Equations
Analysis (mathematics)
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

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