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9780763774929

An Introduction to Analysis

by ; ;
  • ISBN13:

    9780763774929

  • ISBN10:

    0763774928

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2009-08-11
  • Publisher: Jones & Bartlett Learning
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Summary

Part of the Jones and Bartlett International Series in Mathematics Completely revised and update, The second edition of an Introduction to Analysis presents a concise and sharply focused introduction To The basic concepts of analysis from the development of the real numbers through uniform convergences of a sequence of functions, and includes supplementary material on the calculus of functions of several variables and differential equations.  This student-friendly text maintains a cautious and deliberate pace, and examples and figures are used extensively to assist the reader in understanding the concepts and then applying them.  Students will become actively engaged in learning process with a broad and comprehensive collection of problems found at the end of each section. View the detailed Table of Contents here.  

Table of Contents

Prefacep. xi
The Real Numbersp. 1
Setsp. 2
Functionsp. 7
Algebraic and order propertiesp. 12
The positive integersp. 18
The least upper bound axiomp. 24
Sequencesp. 33
Sequences and limitsp. 33
Limit theoremsp. 39
Monotonic sequencesp. 47
Sequences defined inductivelyp. 51
Subsequencesp. 55
Cauchy sequencesp. 65
Infinite limitsp. 68
Functions and Continuityp. 71
Limit of a functionp. 71
Limit theoremsp. 76
Other limitsp. 81
Continuityp. 86
Intermediate values, extreme valuesp. 95
Uniform continuityp. 103
Functions of two variablesp. 109
The Derivativep. 119
Definition of the derivativep. 119
Rules for differentiationp. 127
The Mean Value Theoremp. 132
Inverse functionsp. 143
Differentiability in R2p. 148
The Integralp. 163
The definition of the integralp. 163
Properties of the integralp. 173
Existence theoryp. 182
The Fundamental Theorem of Calculusp. 190
Improper integralsp. 195
Double integralsp. 200
Infinite Seriesp. 213
Basic theoryp. 213
Absolute convergencep. 225
Power seriesp. 233
Taylor seriesp. 247
Sequences and Series of Functionsp. 257
Uniform convergencep. 258
Consequences of uniform convergencep. 270
Two examplesp. 281
Introduction to Differential Equationsp. 289
Elementary first order differential equationsp. 290
Existence and uniquenessp. 298
Power series solutionsp. 307
Appendix: Solutions and Hints for Selected Problemsp. 315
List of Symbolsp. 325
Indexp. 329
Table of Contents provided by Ingram. All Rights Reserved.

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