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Improper Riemann integrals /

Roussos, Ioannis Markos.

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Improper Riemann integrals /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Improper Riemann integrals // Ioannis M. Roussos.
作者:	Roussos, Ioannis Markos.
出版者:	Boca Raton :CRC Press, Taylor & Francis Group, : c2014.,
面頁冊數:	xiv, 675 p. :ill. ;24 cm.
內容註:	Machine generated contents note: 1.Improper Riemann Integrals -- 1.1.Definitions and Examples -- 1.1.1.Applications -- 1.2.Cauchy Principal Value -- 1.3.Some Criteria of Existence -- 2.Real Analysis Techniques -- 2.1.Calculus Techniques -- 2.1.1.Applications -- 2.2.Integrals Dependent on Parameters -- 2.3.Commuting Limits with Integrals and Derivatives -- 2.3.1.Commuting Limits and Integrals -- 2.3.2.Commuting Limits and Derivatives -- 2.4.Double Integral Technique -- 2.5.Frullani Integrals -- 2.6.The Real Gamma and Beta Functions -- 2.6.1.The Gamma Function -- 2.6.2.The Beta Function -- 2.6.3.Applications -- 2.7.A Brief Overview of Laplace Transform -- 2.7.1.Laplace Transform -- 2.7.2.Inverse Laplace Transform -- 2.7.3.Applications -- 3.Complex Analysis Techniques -- 3.1.Basics of Complex Variables -- 3.1.1.Basic Definitions and Operations -- 3.1.2.Representations and Roots of Complex Numbers -- 3.1.3.Square Roots without De Moivre -- 3.2.Power Series -- a Quick Review -- 3.3.Limits, Continuity and Derivatives -- 3.4.Line Integrals in the Complex Plane -- 3.5.Cauchy-Goursat Theorem and Consequences -- 3.5.1.Complex Preliminaries and Notation -- 3.5.2.Cauchy-Goursat Theorem -- 3.5.3.Complex Logarithm -- 3.5.4.Complex Power Functions -- 3.5.5.Properties of Complex Logarithms and Powers -- 3.5.6.Consequence -- 3.5.7.Cauchy Integral Formula -- 3.5.8.Appendix -- 3.6.Roots, Singularities, Residues -- 3.6.1.Definitions, Laurent Expansion and Examples -- 3.6.2.Five Ways to Evaluate Residues -- 3.7.Contour Integration and Integrals -- 3.7.1.Residue Theorem and Examples -- 3.7.2.Contour Integration and Improper Real Integrals -- 3.7.3.Infinite Isolated Singularities and Integrals -- 3.7.4.Infinite Isolated Singularities and Series -- 3.7.5.Fourier Type Integrals -- 3.7.6.Rules and Properties of the Fourier Transform -- 3.7.7.Applications -- 3.7.8.The Fourier Transform with Complex Argument -- 3.7.9.Improper Integrals and Logarithms -- 3.7.10.Application to Inverse
內容註:	Laplace Transform -- 3.8.Definite Integrals with Sines and Cosines -- 3.8.1.Rational Functions of Sines and Cosines -- 3.8.2.Other Techniques with Sines and Cosines -- 3.8.3.Appendix -- 4.List of Non-elementary Integrals and Sums in Text -- 4.1.List of Non-elementary Integrals -- 4.2.List of Non-elementary Sums.
標題:	Riemann integral. -
ISBN:	9781466588073

Improper Riemann integrals /
Roussos, Ioannis Markos.

Improper Riemann integrals /Ioannis M. Roussos. - Boca Raton :CRC Press, Taylor & Francis Group,c2014. - xiv, 675 p. :ill. ;24 cm.

Includes bibliographical references (p. 661-664) and index.

Machine generated contents note: 1.Improper Riemann Integrals -- 1.1.Definitions and Examples -- 1.1.1.Applications -- 1.2.Cauchy Principal Value -- 1.3.Some Criteria of Existence -- 2.Real Analysis Techniques -- 2.1.Calculus Techniques -- 2.1.1.Applications -- 2.2.Integrals Dependent on Parameters -- 2.3.Commuting Limits with Integrals and Derivatives -- 2.3.1.Commuting Limits and Integrals -- 2.3.2.Commuting Limits and Derivatives -- 2.4.Double Integral Technique -- 2.5.Frullani Integrals -- 2.6.The Real Gamma and Beta Functions -- 2.6.1.The Gamma Function -- 2.6.2.The Beta Function -- 2.6.3.Applications -- 2.7.A Brief Overview of Laplace Transform -- 2.7.1.Laplace Transform -- 2.7.2.Inverse Laplace Transform -- 2.7.3.Applications -- 3.Complex Analysis Techniques -- 3.1.Basics of Complex Variables -- 3.1.1.Basic Definitions and Operations -- 3.1.2.Representations and Roots of Complex Numbers -- 3.1.3.Square Roots without De Moivre -- 3.2.Power Series -- a Quick Review -- 3.3.Limits, Continuity and Derivatives -- 3.4.Line Integrals in the Complex Plane -- 3.5.Cauchy-Goursat Theorem and Consequences -- 3.5.1.Complex Preliminaries and Notation -- 3.5.2.Cauchy-Goursat Theorem -- 3.5.3.Complex Logarithm -- 3.5.4.Complex Power Functions -- 3.5.5.Properties of Complex Logarithms and Powers -- 3.5.6.Consequence -- 3.5.7.Cauchy Integral Formula -- 3.5.8.Appendix -- 3.6.Roots, Singularities, Residues -- 3.6.1.Definitions, Laurent Expansion and Examples -- 3.6.2.Five Ways to Evaluate Residues -- 3.7.Contour Integration and Integrals -- 3.7.1.Residue Theorem and Examples -- 3.7.2.Contour Integration and Improper Real Integrals -- 3.7.3.Infinite Isolated Singularities and Integrals -- 3.7.4.Infinite Isolated Singularities and Series -- 3.7.5.Fourier Type Integrals -- 3.7.6.Rules and Properties of the Fourier Transform -- 3.7.7.Applications -- 3.7.8.The Fourier Transform with Complex Argument -- 3.7.9.Improper Integrals and Logarithms -- 3.7.10.Application to Inverse

ISBN: 9781466588073UK76.99

LCCN: 2013037630Subjects--Topical Terms:

753036
Riemann integral.

LC Class. No.: QA311 / .R68 2014

Dewey Class. No.: 515/.43

Improper Riemann integrals /
LDR:02952cam a2200217 a 4500 001 2017594
003 DLC
005 20140826101807.0
008 161003s2014 flua b 001 0 eng
010 $a 2013037630
020 $a 9781466588073 $q (hardcover ; $q alk. paper) : $c UK76.99
020 $a 1466588071 $q (hardcover ; $q alk. paper)
040 $a DLC $b eng $c DLC $d DLC
042 $a pcc
050 0 0 $a QA311 $b .R68 2014
082 0 0 $a 515/.43 $2 23
100 1 $a Roussos, Ioannis Markos. $3 2184898
245 1 0 $a Improper Riemann integrals / $c Ioannis M. Roussos.
260 $a Boca Raton : $b CRC Press, Taylor & Francis Group, $c c2014.
300 $a xiv, 675 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references (p. 661-664) and index.
505 0 $a Machine generated contents note: 1.Improper Riemann Integrals -- 1.1.Definitions and Examples -- 1.1.1.Applications -- 1.2.Cauchy Principal Value -- 1.3.Some Criteria of Existence -- 2.Real Analysis Techniques -- 2.1.Calculus Techniques -- 2.1.1.Applications -- 2.2.Integrals Dependent on Parameters -- 2.3.Commuting Limits with Integrals and Derivatives -- 2.3.1.Commuting Limits and Integrals -- 2.3.2.Commuting Limits and Derivatives -- 2.4.Double Integral Technique -- 2.5.Frullani Integrals -- 2.6.The Real Gamma and Beta Functions -- 2.6.1.The Gamma Function -- 2.6.2.The Beta Function -- 2.6.3.Applications -- 2.7.A Brief Overview of Laplace Transform -- 2.7.1.Laplace Transform -- 2.7.2.Inverse Laplace Transform -- 2.7.3.Applications -- 3.Complex Analysis Techniques -- 3.1.Basics of Complex Variables -- 3.1.1.Basic Definitions and Operations -- 3.1.2.Representations and Roots of Complex Numbers -- 3.1.3.Square Roots without De Moivre -- 3.2.Power Series -- a Quick Review -- 3.3.Limits, Continuity and Derivatives -- 3.4.Line Integrals in the Complex Plane -- 3.5.Cauchy-Goursat Theorem and Consequences -- 3.5.1.Complex Preliminaries and Notation -- 3.5.2.Cauchy-Goursat Theorem -- 3.5.3.Complex Logarithm -- 3.5.4.Complex Power Functions -- 3.5.5.Properties of Complex Logarithms and Powers -- 3.5.6.Consequence -- 3.5.7.Cauchy Integral Formula -- 3.5.8.Appendix -- 3.6.Roots, Singularities, Residues -- 3.6.1.Definitions, Laurent Expansion and Examples -- 3.6.2.Five Ways to Evaluate Residues -- 3.7.Contour Integration and Integrals -- 3.7.1.Residue Theorem and Examples -- 3.7.2.Contour Integration and Improper Real Integrals -- 3.7.3.Infinite Isolated Singularities and Integrals -- 3.7.4.Infinite Isolated Singularities and Series -- 3.7.5.Fourier Type Integrals -- 3.7.6.Rules and Properties of the Fourier Transform -- 3.7.7.Applications -- 3.7.8.The Fourier Transform with Complex Argument -- 3.7.9.Improper Integrals and Logarithms -- 3.7.10.Application to Inverse
505 $a Laplace Transform -- 3.8.Definite Integrals with Sines and Cosines -- 3.8.1.Rational Functions of Sines and Cosines -- 3.8.2.Other Techniques with Sines and Cosines -- 3.8.3.Appendix -- 4.List of Non-elementary Integrals and Sums in Text -- 4.1.List of Non-elementary Integrals -- 4.2.List of Non-elementary Sums.
650 0 $a Riemann integral. $3 753036