Advanced Calculus An Introduction to Linear Analysis

Name: Advanced Calculus An Introduction to Linear Analysis
Price: 74.27 USD
Availability: InStock
ISBN: 9780470232880

ISBN-10: 0470232889

ISBN-13: 9780470232880

Edition: 2008

Authors: Leonard F. Richardson

List price: $172.95

This item qualifies for FREE shipping.

30 day, 100% satisfaction guarantee!

Buy new: $132.35

Marketplace

4 new & used from $74.27

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Description:

Advanced Calculus highlights the connections between calculus and linear algebra and provides a mathematically sophisticated introduction to functional analytic concepts. The book stresses that proofs must be written down, scrutinized step-by-step and rewritten whenever there is doubt. Unlike the competition, this book approaches the rigorous foundations of calculus in a manner that reorients thinking in the directions taken by modern analysis.

Book details

List price: $172.95
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/25/2008
Binding: Hardcover
Pages: 416
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.540
Language: English

Leonard F. Richardson, PhD, is Herbert Huey McElveen Professor and Director of Graduate Studies in Mathematics at Louisiana State University, where he is also Assistant Chair of the Department of Mathematics. Dr. Richardson's research interests include harmonic analysis, homogeneous spaces, and representation theory. He is the author of Advanced Calculus: An Introduction to Linear Analysis, also published by Wiley.



Preface


Acknowledgments


Introduction



Advanced Calculus in One Variable



Real Numbers and Limits of Sequences



The Real Number System


Exercises



Limits of Sequences & Cauchy Sequences


Exercises



The Completeness Axiom and Some Consequences


Exercises



Algebraic Combinations of Sequences


Exercises



The Bolzano-Weierstrass Theorem


Exercises



The Nested Intervals Theorem


Exercises



The Heine-Borel Covering Theorem


Exercises



Countability of the Rational Numbers


Exercises



Test Yourself


Exercises



Continuous Functions



Limits of Functions


Exercises



Continuous Functions


Exercises



Some Properties of Continuous Functions


Exercises



Extreme Value Theorem and Its Consequences


Exercises



The Banach Space C[a, b]


Exercises



Test Yourself


Exercises



Riemann Integral



Definition and Basic Properties


Exercises



The Darboux Integrability Criterion


Exercises



Integrals of Uniform Limits


Exercises



The Cauchy-Schwarz Inequality


Exercises



Test Yourself


Exercises



The Derivative



Derivatives and Differentials


Exercises



The Mean Value Theorem


Exercises



The Fundamental Theorem of Calculus


Exercises



Uniform Convergence and the Derivative


Exercises



Cauchy's Generalized Mean Value Theorem


Exercises



Taylor's Theorem


Exercises



Test Yourself


Exercises



Infinite Series



Series of Constants


Exercises



Convergence Tests for Positive Term Series


Exercises



Absolute Convergence and Products of Series


Exercises



The Banach Space l[subscript 1] and Its Dual Space


Exercises



Series of Functions: The Weierstrass M-Test


Exercises



Power Series


Exercises



Real Analytic Functions and C[superscript infinity] Functions


Exercises



Weierstrass Approximation Theorem


Exercises



Test Yourself


Exercises



Advanced Topics in one Variable



Fourier Series



The Vibrating String and Trigonometric Series


Exercises



Euler's Formula and the Fourier Transform


Exercises



Bessel's Inequality and l[subscript 2]


Exercises



Uniform Convergence & Riemann Localization


Exercises



L[superscript 2]-Convergence & the Dual of l[superscript 2]


Exercises



Test Yourself


Exercises



The Riemann-Stieltjes Integral



Functions of Bounded Variation


Exercises



Riemann-Stieltjes Sums and Integrals


Exercises



Riemann-Stieltjes Integrability Theorems


Exercises



The Riesz Representation Theorem


Exercises



Test Yourself


Exercises



Advanced Calculus in Several Variables



Euclidean Space



Euclidean Space as a Complete Normed Vector Space


Exercises



Open Sets and Closed Sets


Exercises



Compact Sets


Exercises



Connected Sets


Exercises



Test Yourself


Exercises



Continuous Functions on Euclidean Space



Limits of Functions


Exercises



Continuous Functions


Exercises



Continuous Image of a Compact Set


Exercises



Continuous Image of a Connected Set


Exercises



Test Yourself


Exercises



The Derivative in Euclidean Space



Linear Transformations and Norms


Exercises



Differentiable Functions


Exercises



The Chain Rule in Euclidean Space



The Mean Value Theorem



Taylor's Theorem


Exercises



Inverse Functions


Exercises



Implicit Functions


Exercises



Tangent Spaces and Lagrange Multipliers


Exercises



Test Yourself


Exercises



Riemann Integration in Euclidean Space



Definition of the Integral


Exercises



Lebesgue Null Sets and Jordan Null Sets


Exercises



Lebesgue's Criterion for Riemann Integrability


Exercises



Fubini's Theorem


Exercises



Jacobian Theorem for Change of Variables


Exercises



Test Yourself


Exercises



Set Theory



Terminology and Symbols


Exercises



Paradoxes


Problem Solutions


References


Index