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Specifiche dell'oggetto

Condizione
Nuovo: Libro nuovo, intatto e non letto, in perfette condizioni, senza pagine mancanti o ...
Book Title
Problems and Solutions for Undergraduate Analysis
Publication Date
1997-12-19
Pages
368
ISBN
9780387982359

Informazioni su questo prodotto

Product Identifiers

Publisher
Springer New York
ISBN-10
0387982353
ISBN-13
9780387982359
eBay Product ID (ePID)
768496

Product Key Features

Number of Pages
Xii, 368 Pages
Language
English
Publication Name
Problems and Solutions for Undergraduate Analysis
Publication Year
1997
Subject
Probability & Statistics / General, General, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Author
Rami Shakarchi
Series
Undergraduate Texts in Mathematics
Format
Trade Paperback

Dimensions

Item Weight
42 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
98-128337
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
0 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.
Synopsis
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., 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 Number
QA331.5

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