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9780471159964

Fundamental Ideas of Analysis

by
  • ISBN13:

    9780471159964

  • ISBN10:

    0471159964

  • Edition: 1st
  • Format: Paperback
  • Copyright: 1997-09-17
  • Publisher: Wiley

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Supplemental Materials

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Summary

The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

Author Biography

Michael C. Reed is a practicing anthropologist who has worked since 1992 for CSR Incorporated, a Washington, DC, research and evaluation firm. He received his PhD in sociocultural anthropology in 1988, following 15 months of Fulbright fellowship-funded fieldwork in francophone Africa. His dissertation was titled An Ethnohistorical Study of the Political Economy of Ndjole', Gabon. Since 1990, Reed has evaluated several U.S. programs, such as youth substance abuse prevention, school-age child care, secondary education, and community development corporations. He reviews articles for the American Evaluation Association journal Evaluation Practice.

Table of Contents

Preface
CHAPTER 1 Preliminaries
1(26)
1.1 The Real Numbers
1(5)
1.2 Sets and Functions
6(9)
1.3 Cardinality
15(5)
1.4 Methods of Proof
20(7)
CHAPTER 2 Sequences
27(46)
2.1 Convergence
27(8)
2.2 Limit Theorems
35(5)
2.3 Two-state Markov Chains*
40(4)
2.4 Cauchy Sequences
44(8)
2.5 Supremum and Infimum
52(3)
2.6 The Bolzano-Weierstrass Theorem
55(5)
2.7 The Quadratic Map*
60(8)
Projects
68(5)
CHAPTER 3 The Riemann Integral
73(48)
3.1 Continuity
73(7)
3.2 Continuous Functions on Closed Intervals
80(7)
3.3 The Riemann Integral
87(8)
3.4 Numerical Methods*
95(8)
3.5 Discontinuities
103(10)
3.6 Improper Integrals
113(6)
Projects
119(2)
CHAPTER 4 Differentiation
121(42)
4.1 Differentiable Functions
121(8)
4.2 The Fundamental Theorem of Calculus
129(5)
4.3 Taylor's Theorem
134(6)
4.4 Newton's Method*
140(7)
4.5 Inverse Functions
147(4)
4.6 Functions of Two Variables*
151(8)
Projects
159(4)
CHAPTER 5 Sequences of Functions
163(60)
5.1 Pointwise and Uniform Convergence
163(6)
5.2 Limit Theorems
169(6)
5.3 The Supremum Norm
175(8)
5.4 Integral Equations*
183(5)
5.5 The Calculus of Variations*
188(8)
5.6 Metric Spaces
196(7)
5.7 The Contraction Mapping Principle
203(7)
5.8 Normed Linear Spaces*
210(9)
Projects
219(4)
CHAPTER 6 Series of Functions
223(50)
6.1 Lim sup and Lim inf
223(5)
6.2 Series of Real Constants
228(10)
6.3 The Weierstrass M-test
238(7)
6.4 Power Series
245(7)
6.5 Complex Numbers*
252(8)
6.6 Infinite Products and Prime Numbers*
260(10)
Projects
270(3)
CHAPTER 7 Differential Equations*
273(26)
7.1 Local Existence
273(10)
7.2 Global Existence
283(6)
7.3 The Error Estimate for Euler's Method
289(7)
Projects
296(3)
CHAPTER 8 Complex Analysis*
299(24)
8.1 Analytic Functions
299(6)
8.2 Integration on Paths
305(7)
8.3 Cauchy's Theorem
312(8)
Projects
320(3)
CHAPTER 9 Fourier Series*
323(36)
9.1 The Heat Equation
323(8)
9.2 Definitions and Examples
331(6)
9.3 Pointwise Convergence
337(8)
9.4 Mean-square Convergence
345(10)
Projects
355(4)
CHAPTER 10 Probability Theory*
359(44)
10.1 Discrete Random Variables
359(9)
10.2 Coding Theory
368(8)
10.3 Continuous Random Variables
376(10)
10.4 The Variation Metric
386(12)
Projects
398(5)
Bibliography 403(3)
Symbol Index 406(3)
Index 409

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

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