Informazioni su questo prodotto

Product Identifiers

PublisherSpringer New York

ISBN-100387982353

ISBN-139780387982359

eBay Product ID (ePID)768496

Product Key Features

Number of PagesXii, 368 Pages

Publication NameProblems and Solutions for Undergraduate Analysis

LanguageEnglish

SubjectProbability & Statistics / General, General, Mathematical Analysis

Publication Year1997

TypeTextbook

AuthorRami Shakarchi

Subject AreaMathematics

SeriesUndergraduate Texts in Mathematics

FormatTrade Paperback

Dimensions

Item Weight42 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN98-128337

Number of Volumes1 vol.

IllustratedYes

Table Of Content0 Sets and Mappings.- I Real Numbers.- II Limits and Continuous Functions.- III Differentiation.- IV Elementary Functions.- V The Elementary Real Integral.- VI Normed Vector Spaces.- VII Limits.- VIII Compactness.- IX Series.- X The Integral in One Variable.- XI Approximation with Convolutions.- XII Fourier Series.- XIII Improper Integrals.- XIV The Fourier Integral.- XV Functions on n-Space.- XVI The Winding Number and Global Potential Functions.- XVII Derivatives in Vector Spaces.- XVIII Inverse Mapping Theorem.- XIX Ordinary Differential Equations.- XX Multiple Integrals.- XXI Differential Forms.

SynopsisThe present volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis. The wide variety of exercises, which range from computational to more conceptual and which are of vary- ing difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, the inverse and implicit mapping theorem, ordinary differential equations, multiple integrals, and differential forms. My objective is to offer those learning and teaching analysis at the undergraduate level a large number of completed exercises and I hope that this book, which contains over 600 exercises covering the topics mentioned above, will achieve my goal. The exercises are an integral part of Lang's book and I encourage the reader to work through all of them. In some cases, the problems in the beginning chapters are used in later ones, for example, in Chapter IV when one constructs-bump functions, which are used to smooth out singulari- ties, and prove that the space of functions is dense in the space of regu- lated maps. The numbering of the problems is as follows. Exercise IX. 5. 7 indicates Exercise 7, 5, of Chapter IX. Acknowledgments I am grateful to Serge Lang for his help and enthusiasm in this project, as well as for teaching me mathematics (and much more) with so much generosity and patience., The present volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis. The wide variety of exercises, which range from computational to more conceptual and which are of vary ing difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, the inverse and implicit mapping theorem, ordinary differential equations, multiple integrals, and differential forms. My objective is to offer those learning and teaching analysis at the undergraduate level a large number of completed exercises and I hope that this book, which contains over 600 exercises covering the topics mentioned above, will achieve my goal. The exercises are an integral part of Lang's book and I encourage the reader to work through all of them. In some cases, the problems in the beginning chapters are used in later ones, for example, in Chapter IV when one constructs-bump functions, which are used to smooth out singulari ties, and prove that the space of functions is dense in the space of regu lated maps. The numbering of the problems is as follows. Exercise IX. 5. 7 indicates Exercise 7, §5, of Chapter IX. Acknowledgments I am grateful to Serge Lang for his help and enthusiasm in this project, as well as for teaching me mathematics (and much more) with so much generosity and patience., This volume contains all the exercises and their solutions for Lang's second edition of UNDERGRADUATE ANALYSIS. The wide variety of exercises, which range from computational to more conceptual and which are of varying difficulty, cover a wide array of subjects. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning analysis or linear algebra.

LC Classification NumberQA331.5