A Second Course in Mathematical Analysis

Author: J. C. Burkill,H. Burkill

Publisher: Cambridge University Press

ISBN: 9780521523431

Category: Mathematics

Page: 526

View: 6217

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Classic calculus text reissued in Cambridge Mathematical Library. Clear, logical with many examples.

A Second Course in Mathematical Analysis

Author: Dorairaj Somasundaram

Publisher: Alpha Science International Limited

ISBN: 9781842655337

Category: Mathematics

Page: N.A

View: 1097

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A Second Course in Mathematical Analysis makes an in-depth study of Infinite series, Double sequences and series, power series, sequences and series of functions, Functions of bounded variation, Riemann - Stieltjes integrals, Lebesgue integrals, Fourier series, Multivariable differential calculus, Implicit functions and Extremum problems.

A Course of Modern Analysis

Author: E. T. Whittaker,G. N. Watson

Publisher: Cambridge University Press

ISBN: 9780521588072

Category: Mathematics

Page: 608

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This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever.

A First Course in Analysis

Author: John B. Conway

Publisher: Cambridge University Press

ISBN: 1107173140

Category: Mathematics

Page: 375

View: 1522

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This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.

A Treatise on the Theory of Bessel Functions

Author: G. N. Watson

Publisher: Cambridge University Press

ISBN: 9780521483919

Category: Mathematics

Page: 804

View: 9710

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This monumental 1995 treatise by the late Professor G. N. Watson wil be indispensable to mathematicians and physicists.

An Introduction to Harmonic Analysis

Author: Yitzhak Katznelson

Publisher: Cambridge University Press

ISBN: 9780521543590

Category: Mathematics

Page: 314

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First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

Hausdorff Measures

Author: C. A. Rogers

Publisher: Cambridge University Press

ISBN: 9780521624916

Category: Mathematics

Page: 195

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When it was first published this was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. There are three chapters: the first contains an introduction to measure theory, paying particular attention to the study of non-s-finite measures. The second develops the most general aspects of the theory of Hausdorff measures, and the third gives a general survey of applications of Hausdorff measures followed by detailed accounts of two special applications. This edition has a foreword by Kenneth Falconer outlining the developments in measure theory since this book first appeared. Based on lectures given by the author at University College London, this book is ideal for graduate mathematicians with no previous knowledge of the subject, but experts in the field will also want a copy for their shelves.

Waves in Fluids

Author: James Lighthill

Publisher: Cambridge University Press

ISBN: 9780521010450

Category: Mathematics

Page: 504

View: 1675

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This comprehensive text describes the science of waves in fluids.

A First Course in the Numerical Analysis of Differential Equations

Author: A. Iserles

Publisher: Cambridge University Press

ISBN: 0521734908

Category: Mathematics

Page: 459

View: 2976

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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

A Second Course in Linear Algebra

Author: Stephan Ramon Garcia,Roger A. Horn

Publisher: Cambridge University Press

ISBN: 1107103819

Category: Mathematics

Page: 426

View: 7943

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A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.

Spline Functions: Basic Theory

Author: Larry Schumaker

Publisher: Cambridge University Press

ISBN: 1139463438

Category: Mathematics

Page: N.A

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This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.

Probability with Martingales

Author: David Williams

Publisher: Cambridge University Press

ISBN: 1139642987

Category: Mathematics

Page: N.A

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Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital rôle. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.

A Course in Enumeration

Author: Martin Aigner

Publisher: Springer Science & Business Media

ISBN: 3540390359

Category: Mathematics

Page: 565

View: 3080

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Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

Real Analysis

Author: N. L. Carothers

Publisher: Cambridge University Press

ISBN: 9780521497565

Category: Mathematics

Page: 401

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This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists alike, including historical commentary, carefully chosen references, and plenty of exercises.

Methods of Mathematical Physics

Author: Harold Jeffreys,Bertha Jeffreys

Publisher: Cambridge University Press

ISBN: 9780521664028

Category: Mathematics

Page: 718

View: 1384

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This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

Introduction to Model Spaces and their Operators

Author: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

Publisher: Cambridge University Press

ISBN: 1107108748

Category: Mathematics

Page: 335

View: 834

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A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

Markov Chains and Stochastic Stability

Author: Sean P. Meyn,Richard L. Tweedie

Publisher: Springer Science & Business Media

ISBN: 144713267X

Category: Mathematics

Page: 550

View: 8932

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Markov Chains and Stochastic Stability is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. The area of Markov chain theory and application has matured over the past 20 years into something more accessible and complete. It is of increasing interest and importance. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying such stability, provide a new and powerful technique. This does not only affect applications but also the development of the theory itself. The impact of the theory on specific models is discussed in detail, in order to provide examples as well as to demonstrate the importance of these models. Markov Chains and Stochastic Stability can be used as a textbook on applied Markov chain theory, provided that one concentrates on the main aspects only. It is also of benefit to graduate students with a standard background in countable space stochastic models. Finally, the book can serve as a research resource and active tool for practitioners.

LOGIC, SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS

A COMPANION FOR HIGH SCHOOL AND COLLEGE STUDENTS

Author: Brahima MBODJE, Ph.D.

Publisher: Author House

ISBN: 1463429665

Category: Education

Page: 356

View: 4996

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As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

Guide to Analysis

Author: F. Mary Hart

Publisher: Macmillan International Higher Education

ISBN: 1349093904

Category: Applied mathematics

Page: 202

View: 1263

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Guide to Analysis aims to minimise the difficulties which arise from the contrast between analysis and sixth form mathematics. It includes historical notes and anecdotes which will help the reader to appreciate how the subject developed to its present form. Plenty of worked and unworked examples, the latter with hints for solution and answers, are also included.