Foundations of Analysis

ISBN-10: 048646296X
ISBN-13: 9780486462967
Edition: 2nd 2008
List price: $26.95 Buy it from $11.25
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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  More...

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Book details

List price: $26.95
Edition: 2nd
Copyright year: 2008
Publisher: Dover Publications, Incorporated
Publication date: 2/29/2008
Binding: Paperback
Pages: 448
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.232
Language: English

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.

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

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