Foundations of Analysis

Name: Foundations of Analysis
Price: 7.65 USD
Availability: InStock
ISBN: 9780486462967

ISBN-10: 048646296X

ISBN-13: 9780486462967

Edition: 2nd 2008

Authors: David F. Belding, Kevin J. Mitchell

List price: $26.95

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Description:

This treatment develops the real number system and the theory of calculus on the real line, extending the theory to real and complex planes. Designed for students with one year of calculus, it features extended discussions of key ideas and detailed proofs of difficult theorems. Dover (2008) revised second edition of the Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1991 edition.

Book details

List price: $26.95
Edition: 2nd
Copyright year: 2008
Publisher: Dover Publications, Incorporated
Publication date: 2/29/2008
Binding: Paperback
Pages: 427
Size: 6.14" wide x 9.25" long x 0.87" tall
Weight: 1.232
Language: English



Preface



The Real Number System



Introduction



Irrational Numbers



Constructing the Real Numbers



An Axiom System for the Real Numbers



The Heine-Borel Theorem



Functions, Limits, and Continuity



Introduction



Functions



Limits



Limit Theory



Other Types of Limits



Continuity



Continuity on Closed Intervals



Differentiation and Integration



Introduction



The Derivative



Elementary Laws of Differentiation



The Mean Value Theorem



Integration



Properties of the Integral



The Fundamental Theorems of Calculus



Taylor Polynomials



Sequences and Series



Introduction



Infinite Sequences



Monotone and Cauchy Sequences



Infinite Series and Convergence Tests



Absolute and Conditional Convergence



Sequences of Functions



Series of Functions



Calculus in Two Dimensions



Introduction



The Dot Product



Vector-Valued Functions



Functions of a Vector Variable



The Derivative for Vector Functions



Integration



Line Integrals and Green's Theorem



Introduction



The Fundamental Theorem of Calculus: Part I



Line Integrals



The Fundamental Theorem of Calculus: Part II



Green's Theorem



Path Independence and Potential Functions



Complex Analysis



Introduction



The Complex Numbers



Complex Functions and Limits



Differentiability of Complex Functions



The Cauchy-Riemann Equations



Integration



The Cauchy Integral Theorem



The Fundamental Theorem of Algebra



Consequences of the Cauchy Integral Formula


Bibliography


Symbol Index


Index