Introduction to Analysis

ISBN-10: 0763774928
ISBN-13: 9780763774929
Edition: 2nd 2010 (Revised)
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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  More...

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Book details

List price: $176.95
Edition: 2nd
Copyright year: 2010
Publisher: Jones & Bartlett Learning, LLC
Publication date: 7/28/2009
Binding: Hardcover
Pages: 333
Size: 7.50" wide x 9.00" long x 0.75" tall
Weight: 1.584
Language: English

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 students to test themselves on key material.

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

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