A First Look at Numerical Functional Analysis

A First Look at Numerical Functional Analysis

Author: W. W. Sawyer

Publisher: Courier Dover Publications

Published: 2010-12-22

Total Pages: 210

ISBN-13: 0486478823

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Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis. Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence of an iteration, and Rall's ideas of polynomial and quadratic operators. Numerous examples appear throughout the text.


Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author: Haim Brezis

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 600

ISBN-13: 0387709142

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This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.


A First Look at Perturbation Theory

A First Look at Perturbation Theory

Author: James G. Simmonds

Publisher: Courier Corporation

Published: 2013-07-04

Total Pages: 162

ISBN-13: 0486315584

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Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.


Foundations of Mathematical Analysis

Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh

Publisher: Courier Corporation

Published: 2012-09-11

Total Pages: 450

ISBN-13: 0486134776

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Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.


The Surprise Attack in Mathematical Problems

The Surprise Attack in Mathematical Problems

Author: Louis A. Graham

Publisher: Courier Dover Publications

Published: 2017-03-17

Total Pages: 161

ISBN-13: 0486820769

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An unusual problem book that focuses on the method of solution, this collection spotlights 52 problems, each with several approaches to situations involving measurement of geometrical spaces, probabilities, distances, relative motion, more.


Advanced Calculus

Advanced Calculus

Author: H. K. Nickerson

Publisher: Courier Corporation

Published: 2011-08-18

Total Pages: 561

ISBN-13: 0486480909

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"Classroom-tested in a Princeton University honors course, this text offers a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors present a corresponding theory of integration, concluding with a series of applications to analytic functions of complex variables. 1959 edition"--


Tensor Methods in Statistics

Tensor Methods in Statistics

Author: Peter McCullagh

Publisher: Courier Dover Publications

Published: 2018-07-18

Total Pages: 308

ISBN-13: 0486823784

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A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.


Representation Theory of Finite Groups

Representation Theory of Finite Groups

Author: Martin Burrow

Publisher: Courier Corporation

Published: 2014-05-05

Total Pages: 210

ISBN-13: 0486145077

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DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div