Postmodern Analysis [electronic resource] / by Jürgen Jost.
By: Jost, Jürgen [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextSeries: Universitext: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Edition: Third Edition.Description: XV, 375 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540288909.Subject(s): Global analysis (Mathematics)  Differential equations, partial  Analysis  Partial Differential EquationsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

EBOOKS 
ISI Library, Kolkata

Available  EB1049 
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 ArzelaAscoli  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 LpSpaces  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.
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 called “Modern Analysis”. “Modern Analysis” as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonn´ e is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degenerate into a collection of rather unconnected tricks to solve special problems, this de?nitely represented a healthy achievement. 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. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathem ical theory can acquire. However, once this level has been reached, it can be useful to open one’s eyes again to the inspiration coming from concrete external problems.
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Postmodern analysis by Jost Jurgen  
Postmodern analysis by Jost Jurgen 
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