Analysis From Concepts to Applications

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results t...

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Bibliographic Details
Main Author: Penot, Jean-Paul
Format: eBook
Language:English
Published: Cham Springer International Publishing 2016, 2016
Edition:1st ed. 2016
Series:Universitext
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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300 |a XXIII, 669 p. 26 illus  |b online resource 
505 0 |a Sets, Orders, Relations and Measures -- Encounters With Limits -- Elements of Functional Analysis -- Hilbert Spaces -- The Power of Differential Calculus -- A Touch of Convex Analysis -- Integration -- Differentiation and Integration -- Partial Differential Equations -- Evolution Problems -- References -- Index 
653 |a Functional analysis 
653 |a Measure theory 
653 |a Measure and Integration 
653 |a Functional Analysis 
653 |a Partial Differential Equations 
653 |a Partial differential equations 
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520 |a This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character make it appropriate for self-study