Problems and Solutions in Real Analysis

Author: Masayoshi Hata

Publisher: World Scientific Publishing Company

ISBN:

Category: Mathematics

Page: 376

View: 733

This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces. Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references. Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis. Request Inspection Copy Contents:Sequences and LimitsInfinite SeriesContinuous FunctionsDifferentiationIntegrationImproper IntegralsSeries of FunctionsApproximation by PolynomialsConvex FunctionsVarious Proof ζ(2) = π2/6Functions of Several VariablesUniform DistributionRademacher FunctionsLegendre PolynomialsChebyshev PolynomialsGamma FunctionPrime Number TheoremBernoulli NumbersMetric SpacesDifferential Equations Readership: Undergraduates and graduate students in mathematical analysis.

Mathematical Analysis I

Author: Vladimir A. Zorich

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 574

View: 294

This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books. The first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor.

A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis

Author: D. J. H. Garling

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page:

View: 100

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.

Elementary Real Analysis, Second Edition

Author: Brian S. Thomson

Publisher: ClassicalRealAnalysis.com

ISBN:

Category: Mathematics

Page: 638

View: 560

This is the second edition of the text Elementary Real Analysis originally published by Prentice Hall (Pearson) in 2001.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. Differentiation Chapter 8. The IntegralChapter 9. Sequences and series of functionsChapter 10. Power seriesChapter 11. Euclidean Space R^nChapter 12. Differentiation on R^nChapter 13. Metric Spaces

Treatise on Analysis

Author: Jean Dieudonne

Publisher: Academic Press

ISBN:

Category: Science

Page: 387

View: 283

Treatise on Analysis

Real and Complex Analysis

Author: Rajnikant Sinha

Publisher: Springer

ISBN:

Category: Mathematics

Page: 637

View: 863

This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.

Elements of the Theory of Functions and Functional Analysis

Author: Andre? Nikolaevich Kolmogorov

Publisher: Courier Corporation

ISBN:

Category: Mathematics

Page: 288

View: 587

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

Differential and Integral Calculus

Author: Richard Courant

Publisher: John Wiley & Sons

ISBN:

Category: Mathematics

Page: 640

View: 184

The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.

Applied and Computational Complex Analysis, Volume 1

Power Series Integration Conformal Mapping Location of Zero

Author: Peter Henrici

Publisher: John Wiley & Sons

ISBN:

Category: Mathematics

Page: 704

View: 243

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Elementary Real and Complex Analysis

Author: Georgi E. Shilov

Publisher: Courier Corporation

ISBN:

Category: Mathematics

Page: 516

View: 702

Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition.

Introduction to Calculus and Analysis I

Author: Richard Courant

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 661

View: 900

From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficult; most of them supplement the material in the text.

Enumerative Combinatorics:

Author: Richard P. Stanley

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 626

View: 944

"Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets"--

Problems and Solutions in Real Analysis

Author: Masayoshi Hata

Publisher: World Scientific

ISBN:

Category: Mathematics

Page: 292

View: 782

This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.

Philosophical Analysis and Education (International Library of the Philosophy of Education Volume 1)

Author: Reginald Archambault

Publisher: Routledge

ISBN:

Category: Education

Page: 232

View: 545

When originally published in 1965 this book reflected some of the new thinking among philosophers regarding the role of the discipline in its investigation of central issues in educaton. The essays are grouped into four major sections: The Nature and Function of Educational Theory; The Context of Educational Discussion; Conceptions of Teaching; and The Essence of Education. The concepts dealt with are of the first importance to any practical or theoretical discussion in education and the editor provides a generous introduction to the essays to aid the reader in his analysis of the issues.

Numerical Solution of Ordinary Differential Equations

Author: Kendall Atkinson

Publisher: John Wiley & Sons

ISBN:

Category: Mathematics

Page: 272

View: 604

A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Human Rights and the Private Sphere Vol 1

A Comparative Study

Author: Jörg Fedtke

Publisher: Routledge

ISBN:

Category: Law

Page: 608

View: 376

Particularly valuable for both academics and practitioners, Human Rights and the Private Sphere: A Comparative Study analyzes the interaction between constitutional rights, freedoms and private law. Focusing primarily on civil and political rights, an international team of constitutional and private law experts have contributed a collection of chapters, each based around a different jurisdiction. They include Denmark, France, Germany, India, Ireland, Israel, Italy, New Zealand, the UK, the US, the European Convention for the Protection of Human Rights and Fundamental Freedoms and the European Union. As well as exploring, chapter by chapter, the key topics and debates in each jurisdiction, a comparative analysis draws the sections together; setting-out the common features and differences in the jurisdictions under review and identifies some common trends in this important area of the law. Cross-references between the various chapters and an appendix containing relevant legislative material and translated quotations from important court decisions makes this volume a valuable tool for those studying and working in the field of international human rights law.

Environmental Management in Practice: Vol 1

Instruments for Environmental Management

Author: Paul Compton

Publisher: Routledge

ISBN:

Category: Social Science

Page: 544

View: 523

Focuses on the instruments and tools currently available to the environmental manager. A theoretical background to the instruments is given together with an overview of those instruments that are in common use today, with particular attention to the physical, economic, legislative and communication instruments.