Way of Analysis

ISBN-10: 0763714976

ISBN-13: 9780763714970

Edition: 2000 (Revised)

List price: $278.95 Buy it from $139.46
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Description: 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.

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Book details

List price: $278.95
Copyright year: 2000
Publisher: Jones & Bartlett Learning, LLC
Publication date: 6/2/2000
Binding: Paperback
Pages: 739
Size: 6.00" wide x 9.25" long x 1.25" tall
Weight: 2.090
Language: English

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
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