Postmodern Analysis

AvJürgen Jost

Häftad, Engelska, 2005

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Beskrivning

In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while.

Produktinformation

Utgivningsdatum:2005-08-01
Mått:155 x 235 x 30 mm
Vikt:596 g
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:375
Upplaga:3
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540258308
Översättare:H. Azad

Utforska kategorier

Innehållsförteckning

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.