Real Mathematical Analysis

ISBN-10: 0387952977

ISBN-13: 9780387952970

Edition: 2002

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In this introduction to undergraduate real analysis the author stresses the importance of pictures in mathematics and hard problems.
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Book details

List price: $69.95
Copyright year: 2002
Publisher: Springer
Publication date: 11/14/2003
Binding: Hardcover
Pages: 440
Size: 6.50" wide x 9.75" long x 1.25" tall
Weight: 1.980
Language: English

Real Numbers
Preliminaries
Cuts
Euclidean Space
Cardinality
Comparing Cardinalities
The Skeleton of Calculus
Exercises
A Taste of Topology
Metric Space Concepts
Compactness
Connectedness
Coverings
Cantor Sets
Cantor Set Lore
Completion
Exercises
Functions of a Real Variable
Differentiation
Riemann Integration
Series
Exercises
Function Spaces
Uniform Convergence and C[superscript 0 a,b]
Power Series
Compactness and Equicontinuity in C[superscript 0]
Uniform Approximation in C[superscript 0]
Contractions and ODE's
Analytic Functions
Nowhere Differentiable Continuous Functions
Spaces of Unbounded Functions
Exercises
Multivariable Calculus
Linear Algebra
Derivatives
Higher derivatives
Smoothness Classes
Implicit and Inverse Functions
The Rank Theorem
Lagrange Multipliers
Multiple Integrals
Differential Forms
The General Stokes' Formula
The Brouwer Fixed Point Theorem
Perorations of Dieudonne
The History of Cavalieri's Principle
A Short Excursion into the Complex Field
Polar Form
Determinants
Exercises
Lebesgue Theory
Outer measure
Measurability
Regularity
Lebesgue integrals
Lebesgue integrals as limits
Italian Measure Theory
Vitali coverings and density points
Lebesgue's Fundamental Theorem of Calculus
Lebesgue's Last Theorem
Translations and Nonmeasurable sets
The Banach-Tarski Paradox
Riemann integrals as undergraphs
Littlewood's Three Principles
Roundness
Money
Suggested Reading
Bibliography
Exercises
Index
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