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 - proach to analysis presented here from what has by its protagonists been call...
| Uniform Title: | Postmoderne Analysis. English |
|---|---|
| Main Author: | Jost, Jürgen, 1956- |
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English German |
| Published: |
Berlin :
Springer,
©2005.
Berlin : [2005] |
| Physical Description: |
1 online resource (xv, 371 pages) : illustrations. |
| Edition: | 3rd ed. |
| Series: |
Universitext.
|
| Subjects: |
Table of Contents:
- Calculus for Functions of One Variable
- Prerequisites
- Limits and Continuity of Functions
- Differentiability
- Characteristic Properties of Differentiable Functions. Differential Equations
- The Banach Fixed Point Theorem. The Concept of Banach Space
- Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
- Integrals and Ordinary Differential Equations
- Topological Concepts
- Metric Spaces: Continuity, Topological Notions, Compact Sets
- Calculus in Euclidean and Banach Spaces
- Differentiation in Banach Spaces
- Differential Calculus in $$\mathbb{R}$$ d
- The Implicit Function Theorem. Applications
- Curves in $$\mathbb{R}$$ d. Systems of ODEs
- The Lebesgue Integral
- Preparations. Semicontinuous Functions
- The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets
- Lebesgue Integrable Functions and Sets
- Null Functions and Null Sets. The Theorem of Fubini
- The Convergence Theorems of Lebesgue Integration Theory
- Measurable Functions and Sets. Jensen's Inequality. The Theorem of Egorov
- The Transformation Formula
- and Sobolev Spaces
- The Lp-Spaces
- Integration by Parts. Weak Derivatives. Sobolev Spaces
- to the Calculus of Variations and Elliptic Partial Differential Equations
- Hilbert Spaces. Weak Convergence
- Variational Principles and Partial Differential Equations
- Regularity of Weak Solutions
- The Maximum Principle
- The Eigenvalue Problem for the Laplace Operator.