| 000 | 04657nam a2200709 i 4500 | ||
|---|---|---|---|
| 001 | 6812532 | ||
| 003 | IEEE | ||
| 005 | 20200413152900.0 | ||
| 006 | m eo d | ||
| 007 | cr cn |||m|||a | ||
| 008 | 110219s2011 caua foab 001 0 eng d | ||
| 020 | _a9781608456147 (electronic bk.) | ||
| 020 | _z9781608456130 (pbk.) | ||
| 024 | 7 |
_a10.2200/S00327ED1V01Y201101MAS009 _2doi |
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| 035 | _a(CaBNVSL)gtp00546204 | ||
| 035 | _a(OCoLC)707877354 | ||
| 040 |
_aCaBNVSL _cCaBNVSL _dCaBNVSL |
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| 050 | 4 |
_aQA311 _b.K725 2011 |
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| 082 | 0 | 4 |
_a515.42 _222 |
| 100 | 1 |
_aKrantz, Steven G. _q(Steven George), _d1951- |
|
| 245 | 1 | 4 |
_aThe integral _h[electronic resource] : _ba crux for analysis / _cSteven G. Krantz. |
| 260 |
_aSan Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : _bMorgan & Claypool, _cc2011. |
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| 300 |
_a1 electronic text (xii, 93 p.) : _bill., digital file. |
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| 490 | 1 |
_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 9 |
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| 538 | _aMode of access: World Wide Web. | ||
| 538 | _aSystem requirements: Adobe Acrobat Reader. | ||
| 500 | _aPart of: Synthesis digital library of engineering and computer science. | ||
| 500 | _aSeries from website. | ||
| 504 | _aIncludes bibliographical references (p. 87) and index. | ||
| 505 | 0 | _a1. 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 -- | |
| 505 | 0 | _a2. 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 -- | |
| 505 | 0 | _a3. 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 -- | |
| 505 | 0 | _a4. Comparison of the Riemann and Lebesgue integrals -- Any Riemann integrable function is Lebesgue integrable -- Exercises -- | |
| 505 | 0 | _a5. Other theories of the integral -- The Daniell integral -- The Riemann-Stieltjes integral -- The Henstock-Kurzweil integral -- Hausdorff measure -- Haar measure -- The fundamental theorem -- Exercises -- | |
| 505 | 0 | _aBibliography -- Author's biography -- Index. | |
| 506 | 1 | _aAbstract freely available; full-text restricted to subscribers or individual document purchasers. | |
| 510 | 0 | _aCompendex | |
| 510 | 0 | _aINSPEC | |
| 510 | 0 | _aGoogle scholar | |
| 510 | 0 | _aGoogle book search | |
| 520 | 3 | _aThis 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. | |
| 530 | _aAlso available in print. | ||
| 588 | _aTitle from PDF t.p. (viewed on February 19, 2011). | ||
| 650 | 0 | _aIntegral theorems. | |
| 650 | 0 | _aRiemann integral. | |
| 650 | 0 | _aLebesgue integral. | |
| 653 | _aIntegral | ||
| 653 | _aRiemann integral | ||
| 653 | _aLebesgue integral | ||
| 653 | _aHenstock integral | ||
| 653 | _aDaniell integral | ||
| 653 | _aStieltjes integral | ||
| 653 | _aLimiting processes | ||
| 653 | _aInequalities | ||
| 653 | _aMeasure | ||
| 653 | _aMeasurable function | ||
| 653 | _aLebesgue theorems | ||
| 776 | 0 | 8 |
_iPrint version: _z9781608456130 |
| 830 | 0 | _aSynthesis digital library of engineering and computer science. | |
| 830 | 0 |
_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 9. |
|
| 856 | 4 | 2 |
_3Abstract with links to resource _uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=6812532 |
| 999 |
_c561815 _d561815 |
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