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Functions, Spaces, and Expansions: Mathematical Tools in Physics and Engineering (Applied and Numerical Harmonic Analysis)

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Functions, Spaces, and Expansions: Mathematical Tools in Physics and Engineering (Applied and Numerical Harmonic Analysis) Cover

 

Synopses & Reviews

Publisher Comments:

This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. A central theme of the book is the structure of various vector spaces--most importantly, Hilbert spaces--and expansions of elements in these spaces in terms of bases. Key topics and features include: * More than 150 exercises * Abstract and normed vector spaces * Approximation in normed vector spaces * Hilbert and Banach spaces * General bases and orthonormal bases * Linear operators on various normed spaces * The Fourier transform, including the discrete Fourier transform * Wavelets and multiresolution analysis * B-splines * Sturm-Liouville problems As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required. Functions, Spaces, and Expansions is the main textbook for the e-course Mathematics 4: Real Analysis currently being taught at the Technical University of Denmark. Please click the "Course Materials" link on the right to access videos of the lectures, problem sheets, and solutions to selected exercises.

Synopsis:

This text presents a detailed exposition of key mathematical tools in analysis. Each topic covered was chosen because it plays a role beyond the field of pure mathematics, so the text is useful in exploring the computational areas of physics and engineering.

Table of Contents

Preface.- Prologue.- Mathematical Background.- Normed Vector Spaces.- Banach Spaces.- Hilbert Spaces.- The L^p-spaces.- The Hilbert Space L^2.- The Fourier Transform.- An Introduction to Wavelet Analysis.- A Closer Look on Multiresolution Analysis.- B-splines.- Special Functions.- Appendix A.- Appendix B.- List of Symbols.- References.- Index.

Product Details

ISBN:
9780817649791
Author:
Christensen, Ole
Publisher:
Birkhauser
Author:
Christensen, OLE
Location:
Boston, MA
Subject:
Functional Analysis
Subject:
Mathematical Analysis
Subject:
Computer Science
Subject:
B-splines
Subject:
Banach spaces
Subject:
Fourier transform
Subject:
Hermite polynomials.
Subject:
Hilbert spaces.
Subject:
Laguerre polynomials.
Subject:
Legendre polynomials
Subject:
Sturm "Liouville problems
Subject:
Weierstrass theorem.
Subject:
abstract vector spaces
Subject:
Multiresolution analysis
Subject:
normed vector spaces
Subject:
orthonormal bases
Subject:
WAVELET ANALYSIS
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
mathematical methods in physics
Subject:
Special functions
Subject:
Fourier analysis
Subject:
Computational science and engineering
Subject:
Mathematics : Functional Analysis
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Engineering mathematics
Subject:
Mathematical Physics
Subject:
Functions, special
Copyright:
Edition Description:
2010
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
20100615
Binding:
HARDCOVER
Language:
English
Pages:
285
Dimensions:
235 x 155 mm 1280 gr

Related Subjects

Computers and Internet » Computers Reference » General
Computers and Internet » Personal Computers » General
Reference » Science Reference » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Physics » General

Functions, Spaces, and Expansions: Mathematical Tools in Physics and Engineering (Applied and Numerical Harmonic Analysis) New Hardcover
0 stars - 0 reviews
$56.95 In Stock
Product details 285 pages Birkhauser - English 9780817649791 Reviews:
"Synopsis" by , This text presents a detailed exposition of key mathematical tools in analysis. Each topic covered was chosen because it plays a role beyond the field of pure mathematics, so the text is useful in exploring the computational areas of physics and engineering.
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