A Second Course on Real Functions

Author: A. C. M. van Rooij,W. H. Schikhof

Publisher: CUP Archive

ISBN: 9780521283618

Category: Mathematics

Page: 200

View: 6218

When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this.
Posted in Mathematics

A Second Course in Mathematical Analysis

Author: J. C. Burkill,H. Burkill

Publisher: Cambridge University Press

ISBN: 9780521523431

Category: Mathematics

Page: 526

View: 5546

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

A Second Course in Complex Analysis

Author: William A. Veech

Publisher: Courier Corporation

ISBN: 048615193X

Category: Mathematics

Page: 256

View: 5318

Geared toward upper-level undergraduates and graduate students, this clear, self-contained treatment of important areas in complex analysis is chiefly classical in content and emphasizes geometry of complex mappings. 1967 edition.
Posted in Mathematics

A Companion to Analysis

A Second First and First Second Course in Analysis

Author: Thomas William Körner

Publisher: American Mathematical Soc.

ISBN: 0821834479

Category: Mathematics

Page: 590

View: 4014

This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.
Posted in Mathematics

Function Theory on Planar Domains

A Second Course in Complex Analysis

Author: Stephen D. Fisher

Publisher: Courier Corporation

ISBN: 0486151107

Category: Mathematics

Page: 288

View: 8647

This treatment of complex analysis focuses on function theory on a finitely connected planar domain. It emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. 1983 edition.
Posted in Mathematics

A Primer of Real Functions

Author: Ralph P. Boas,Harold P. Boas

Publisher: Cambridge University Press

ISBN: 9780883850299

Category: Mathematics

Page: 305

View: 1371

Revised edition of a classic Carus monograph with a new chapter on integration and its applications.
Posted in Mathematics

Calculus Deconstructed

A Second Course in First-Year Calculus

Author: Zbigniew H. Nitecki

Publisher: MAA

ISBN: 9780883857564

Category: Mathematics

Page: 491

View: 6270

A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous experience of calculus techniques. This book can be used as a textbook for an undergraduate course on calculus or as a reference for self-study.
Posted in Mathematics

Real Mathematical Analysis

Author: Charles Chapman Pugh

Publisher: Springer

ISBN: 3319177710

Category: Mathematics

Page: 478

View: 5785

Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitali’s Covering Lemma, density points — which are rarely treated in books at this level — and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.
Posted in Mathematics

The Theory of Functions of Real Variables

Second Edition

Author: Lawrence M Graves

Publisher: Courier Corporation

ISBN: 0486158136

Category: Mathematics

Page: 400

View: 1788

This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Posted in Mathematics

A First Course in Sobolev Spaces: Second Edition

Author: Giovanni Leoni

Publisher: American Mathematical Soc.

ISBN: 1470429217

Category: Sobolev spaces

Page: 734

View: 504

This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.
Posted in Sobolev spaces

Introduction to Real Analysis

Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 0486131920

Category: Mathematics

Page: 384

View: 1359

This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
Posted in Mathematics

Complex Function Theory

Author: Donald Sarason

Publisher: American Mathematical Soc.

ISBN: 0821844288

Category: Mathematics

Page: 163

View: 1354

Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
Posted in Mathematics

A Second Course in Elementary Differential Equations

Author: Paul Waltman

Publisher: Elsevier

ISBN: 1483276600

Category: Mathematics

Page: 272

View: 9310

A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.
Posted in Mathematics

A First Course in Real Analysis

Author: M.H. Protter,C.B. Jr. Morrey

Publisher: Springer Science & Business Media

ISBN: 1461599903

Category: Mathematics

Page: 507

View: 8638

The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.
Posted in Mathematics

A second course in algebra

Author: Webster Wells

Publisher: N.A


Category: Algebra

Page: 311

View: 7898

Posted in Algebra

A second course in linear algebra

Author: William Clough Brown

Publisher: Wiley-Interscience

ISBN: 9780471626022

Category: Mathematics

Page: 264

View: 8815

Posted in Mathematics

Scenes from the History of Real Functions

Author: F.A. Medvedev

Publisher: Birkhäuser

ISBN: 3034886608

Category: Science

Page: 265

View: 4297

To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.
Posted in Science

A second course in calculus

Author: John Meigs Hubbell Olmsted

Publisher: Irvington Pub


Category: Mathematics

Page: 391

View: 3365

Posted in Mathematics

Linear Algebra and Matrices: Topics for a Second Course

Author: Helene Shapiro

Publisher: American Mathematical Soc.

ISBN: 1470418525

Category: Mathematics

Page: 317

View: 6784

Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.
Posted in Mathematics