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The Way of Analysis : Jones and Bartlett Books in Mathematics - Robert S. Strichartz

The Way of Analysis

Jones and Bartlett Books in Mathematics

Paperback

Published: 16th June 2000
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The Way of Analysis  gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral.  the text provides proofs of all main results, As well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.

Preface:
Preliminaries
The Logic of Quantifiers
Infinite Sets
Proofs
The Rational Number System
The Axiom of Choice
Construction of the Real Number System
Cauchy Sequences
The Reals as an Ordered Field
Limits and Completeness
Other Versions and Visions
Summary
The Theory of Limits
Open Sets and Closed Sets
Compact Sets
Summary
Continuous Functions
Concepts of Continuity
Properties of Continuous Functions
Summary
Differential Calculus
Concepts of the Derivative
Properties of the Derivative
The Calculus of Derivatives
Higher Derivatives and Taylor's Theorem
Summary
Integral Calculus
Integrals of Continuous Functions
The Riemann Integral
Improper Integrals
Summary
Sequences and Series of Functions
Complex Numbers
Numerical Series and Sequences
Uniform Convergence
Power Series
Approximation by Polynomials
Equicontinuity
Summary
Transcendental Functions
The Exponential and Logarithm
Trigonometric Functions
Summary
Euclidean Space and Metric Spaces
Structures on Euclidean Space
Topology of Metric Spaces
Continuous Functions on Metric Spaces
Summary
Differential Calculus in Euclidean Space
The Differential
Higher Derivatives
Summary
Ordinary Differential Equations
Existence and Uniqueness
Other Methods of Solution
Vector Fields and Flows
Summary
Fourier Series
Origins of Fourier Series
Convergence of Fourier Series
Summary
Implicit Functions, Curves, and Surfaces
The Implicit Function Theorem
Curves and Surfaces}
Maxima and Minima on Surfaces
Arc Length
Summary
The Lebesgue
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780763714970
ISBN-10: 0763714976
Series: Jones and Bartlett Books in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 739
Published: 16th June 2000
Publisher: Jones and Bartlett Publishers, Inc
Country of Publication: US
Dimensions (cm): 23.5 x 15.24  x 3.18
Weight (kg): 1.0
Edition Type: Revised