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Conway - A first course in analysis

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Conway A first course in analysis
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    A first course in analysis
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The real numbers -- Differentiation -- Integration -- Sequences of functions -- Metric and Euclidean spaces -- Differentiation in higher dimensions -- Integration in higher dimensions -- Curves and surfaces -- Differential forms.;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. -- Provided by publisher.

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A First Course in Analysis This rigorous textbook is intended for a year-long - photo 1
A First Course in Analysis
This rigorous textbook is intended for a year-long analysis or advanced calculuscourse for advanced undergraduate or beginning graduate students. Starting withdetailed, slow-paced proofs that allow students to acquire facility in reading andwriting proofs, it clearly and concisely explains the basics of differentiation andintegration of functions of one and several variables, and covers the theorems ofGreen, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linearalgebra topics are reviewed right before they are needed, making the materialaccessible to students from diverse backgrounds. Abstract topics are preceded byconcrete examples to facilitate understanding e.g. before introducing differentialforms, the text examines low-dimensional examples. The meaning and importanceof results are thoroughly discussed, and numerous exercises of varying difficulty givestudents ample opportunity to test and improve their knowledge of this difficult yetvital subject.

John B. Conway is Professor Emeritus of Mathematics at George WashingtonUniversity. He is the author of eleven books, including Mathematical Connections: ACapstone Course , A Course in Functional Analysis , and the two-volume Functionsof One Complex Variable .

Cambridge Mathematical Textbooks

Cambridge Mathematical Textbooks is a program of undergraduate and beginning graduate level textbooks for corecourses, new courses, and interdisciplinary courses in pure and applied mathematics. These texts provide motivation with plenty of exercises of varying difficulty,interesting examples, modern applications, and unique approaches to the material.
Advisory Board
John B. Conway, George Washington University
Gregory F. Lawler, University of Chicago
John M. Lee, University of Washington
John Meier, Lafayette College
Lawrence C. Washington, University of Maryland, College Park

A complete list of books in the series can be found at www.cambridge.org/mathematics Recent titles include the following:

Chance, Strategy, and Choice: An Introduction to the Mathematics of Games and Elections , S. B. Smith
Set Theory: A First Course , D. W. Cunningham
Chaotic Dynamics: Fractals, Tilings, and Substitutions , G. R. Goodson
Introduction to Experimental Mathematics , S. Eilers & R. Johansen
A Second Course in Linear Algebra , S. R. Garcia & R. A. Horn
Exploring Mathematics: An Engaging Introduction to Proof , J. Meier & D. Smith
A First Course in Analysis , J. B. Conway

This is an excellent text for a first course in analysis in one and several variablesfor students who know some linear algebra. The book starts with the realnumbers, does differentiation and integration first in one variable, then in several,and finally covers differential forms and Stokes theorem. The style is friendly andconversational, and hews to the principal of going from the specific to thegeneral, making it a pleasure to read.

John McCarthy, Washington University in St. Louis

Conways previous texts are all considered classics. A First Course inAnalysis is destined to be another. It is written in the same friendly, yetrigorous, style that his readers know and love. Instructors seeking the breadthand depth of Rudin, but in a less austere and more accessible form, have foundtheir book.

Stephan Ramon Garcia, PomonaCollege

This is a beautiful yet practical introduction to rigorous analysis at the seniorundergraduate level, written by a master expositor.

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