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 protagonist...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Jost, Jürgen (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
Edición:3rd ed. 2005.
Colección:Universitext,
Temas:
Mathematical analysis.
Differential equations.
Analysis.
Differential Equations.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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