Introduction to Analysis

Name: Introduction to Analysis
Price: 142.61 USD
Availability: InStock
ISBN: 9780763774929

ISBN-10: 0763774928

ISBN-13: 9780763774929

Edition: 2nd 2010 (Revised)

Authors: Gerald G. Bilodeau, Paul R. Thie, G. E. Keough

List price: $215.95

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Description:

Part of the Jones and Bartlett International Series in Advanced Mathematics Completely revised and update, the second edition of An Introduction to Analysis presents a clear and comprehensive introduction to the basic concepts of analysis. It is designed for a one-term course, following a calculus sequence, at the undergraduate level. The authors present important topics from calculus in a rigorous manner and develop students' ability to work in an abstract setting with precise definitions and complete proofs. Numerous examples are presented to demonstrate abstract statements in simpler numerical settings. A broad collection of accessible problems, found at the end of each section, ask…

Book details

List price: $215.95
Edition: 2nd
Copyright year: 2010
Publisher: Jones & Bartlett Learning, LLC
Publication date: 8/11/2009
Binding: Hardcover
Pages: 334
Size: 7.50" wide x 9.00" long x 0.75" tall
Weight: 1.892
Language: English

David B. Morris is University Professor of English at the University of Virginia. He is the author of many books, including The Culture of Pain .



Preface



The Real Numbers



Sets



Functions



Algebraic and order properties



The positive integers



The least upper bound axiom



Sequences



Sequences and limits



Limit theorems



Monotonic sequences



Sequences defined inductively



Subsequences



Cauchy sequences



Infinite limits



Functions and Continuity



Limit of a function



Limit theorems



Other limits



Continuity



Intermediate values, extreme values



Uniform continuity



Functions of two variables



The Derivative



Definition of the derivative



Rules for differentiation



The Mean Value Theorem



Inverse functions



Differentiability in R2



The Integral



The definition of the integral



Properties of the integral



Existence theory



The Fundamental Theorem of Calculus



Improper integrals



Double integrals



Infinite Series



Basic theory



Absolute convergence



Power series



Taylor series



Sequences and Series of Functions



Uniform convergence



Consequences of uniform convergence



Two examples



Introduction to Differential Equations



Elementary first order differential equations



Existence and uniqueness



Power series solutions


Appendix: Solutions and Hints for Selected Problems


List of Symbols


Index