Way of Analysis

Name: Way of Analysis
Price: 36.45 USD
Availability: InStock
ISBN: 9780763714970

ISBN-10: 0763714976

ISBN-13: 9780763714970

Edition: 2000 (Revised)

Authors: Robert S. Strichartz

List price: $330.95

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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.

Book details

List price: $330.95
Copyright year: 2000
Publisher: Jones & Bartlett Learning, LLC
Publication date: 6/16/2000
Binding: Paperback
Pages: 739
Size: 6.00" wide x 9.00" long x 1.50" tall
Weight: 2.068



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