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Postmodern Analysis

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Cover of 'Postmodern Analysis'

Table of Contents

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    Book Overview
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    Chapter 1 Prerequisites
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    Chapter 2 Limits and Continuity of Functions
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    Chapter 3 Differentiability
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    Chapter 4 Characteristic Properties of Differentiable Functions. Differential Equations
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    Chapter 5 The Banach Fixed Point Theorem. The Concept of Banach Space
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    Chapter 6 Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
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    Chapter 7 Integrals and Ordinary Differential Equations
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    Chapter 8 Metric Spaces: Continuity, Topological Notions, Compact Sets
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    Chapter 9 Differentiation in Banach Spaces
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    Chapter 10 Differential Calculus in ℝ d
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    Chapter 11 The Implicit Function Theorem. Applications
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    Chapter 12 Curves in ℝ d . Systems of ODEs
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    Chapter 13 Preparations. Semicontinuous Functions
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    Chapter 14 The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets
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    Chapter 15 Lebesgue Integrable Functions and Sets
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    Chapter 16 Null Functions and Null Sets. The Theorem of Fubini
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    Chapter 17 The Convergence Theorems of Lebesgue Integration Theory
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    Chapter 18 Measurable Functions and Sets. Jensen’s Inequality. The Theorem of Egorov
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    Chapter 19 The Transformation Formula
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    Chapter 20 The L p -Spaces
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    Chapter 21 Integration by Parts. Weak Derivatives. Sobolev Spaces
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    Chapter 22 Hilbert Spaces. Weak Convergence
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    Chapter 23 Variational Principles and Partial Differential Equations
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    Chapter 24 Regularity of Weak Solutions
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    Chapter 25 The Maximum Principle
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    Chapter 26 The Eigenvalue Problem for the Laplace Operator
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Title
Postmodern Analysis
Published by
Springer Berlin Heidelberg, January 2003
DOI 10.1007/978-3-662-05306-5
ISBNs
978-3-54-043873-1, 978-3-66-205306-5
Authors

Jürgen Jost, Jost, Jürgen

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