Closer and Closer Introducing Real Analysis

ISBN-10: 0763735930

ISBN-13: 9780763735937

Edition: 2008

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Description:

Closer and Closer: Introducing Real Analysisis the ideal first introduction to real analysis for upper-level undergraduate Math majors. The text is divided into two main parts; the core material of the subjectis covered in Chapters 1-13, and a series of cases, examples, applications, and projects, collectively called Excursionsform the second half of the book. These Excursions are designed to bring the concepts of real analysis to light and to allow students to work through numerous interesting problems with ease.
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Book details

Copyright year: 2008
Publisher: Jones & Bartlett Learning, LLC
Publication date: 7/16/2007
Binding: Paperback
Pages: 438
Size: 7.50" wide x 9.00" long x 1.25" tall
Weight: 2.046
Language: English

Basic building blocks
The real numbers
Measuring distances
Sets and limits
Continuity
Real-valued functions
Completeness
Compactness
Connectedness
Differentiation of functions of one real variable
Iteration and the contraction mapping theorem
The riemann integral
Sequences of functions
Differentiating f : R[superscript n] [approaches] R[superscript m]
Truth and provability
Number properties
Exponents
Sequences in R and R[superscript n]
Limits of functions from R to R
Doubly indexed sequences
Subsequences and convergence
Series of real numbers
Probing the definition of the riemann integral
Power series
Everywhere continuous, nowhere differentiable
Newton's method
The implicit function theorem
Spaces of continuous 'functions
Solutions to differential equations
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