The integral : a crux for analysis /
By: Krantz, Steven G. (Steven George).
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mathematics and statistics: # 9.Publisher: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, c2011Description: 1 electronic text (xii, 93 p.) : ill., digital file.ISBN: 9781608456147 (electronic bk.).Subject(s): Integral theorems | Riemann integral | Lebesgue integral | Integral | Riemann integral | Lebesgue integral | Henstock integral | Daniell integral | Stieltjes integral | Limiting processes | Inequalities | Measure | Measurable function | Lebesgue theoremsDDC classification: 515.42 Online resources: Abstract with links to resource Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE315 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Series from website.
Includes bibliographical references (p. 87) and index.
1. Introduction -- What is an integral -- What is the Riemann integral -- What is the Riemann integral good for -- What is the Riemann integral not good for -- What is the Lebesgue integral -- What is the Lebesgue integral good for -- What is the Lebesgue not good for -- Exercises --
2. The Riemann integral -- The definition -- Properties of the Riemann integral -- Characterization of Riemann integrability -- The fundamental theorem of calculus -- Numerical techniques of integration -- Introduction -- The method of rectangles -- The trapezoidal rule -- Simpson's rule -- Integration by parts -- Exercises --
3. The Lebesgue integral -- Elementary measure theory -- Measurable sets -- The Lebesgue integral -- Three big theorems about the Lebesgue integral -- The Lebesgue spaces LP -- The Riesz representation theorem -- Product integration: Fubini's theorem -- Three principles of Littlewood -- Differentiation of integrals: covering lemmas and the Lebesgue theorem -- Basic ideas -- The maximal function -- The concept of convergence in measure -- Functions of bounded variation and absolute continuity -- Exercises --
4. Comparison of the Riemann and Lebesgue integrals -- Any Riemann integrable function is Lebesgue integrable -- Exercises --
5. Other theories of the integral -- The Daniell integral -- The Riemann-Stieltjes integral -- The Henstock-Kurzweil integral -- Hausdorff measure -- Haar measure -- The fundamental theorem -- Exercises --
Bibliography -- Author's biography -- Index.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
Compendex
INSPEC
Google scholar
Google book search
This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics.
Also available in print.
Title from PDF t.p. (viewed on February 19, 2011).
There are no comments for this item.