Real Mathematical Analysis

Name: Real Mathematical Analysis
Availability: InStock
ISBN: 9780387952970

ISBN-10: 0387952977

ISBN-13: 9780387952970

Edition: 2002

Authors: Charles Chapman Pugh, F. W. Gehring, P. R. Halmos

List price: $69.95

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Description:

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

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: 1.694
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