000			03445cam a2200337 i 4500
001			17887834
003			OSt
005			20260513142931.0
008			130916t20142014flu b 001 0 eng
010			_a 2013037630
020			_a9781032032054 (pbk.)
035			_a17887834
040			_aDLC _beng _cJKRC _erda _dDLC
082	0	0	_223 _a515.43 _bROU.I
100	1		_aRoussos, Ioannis Markos. _eauthor _939590
245	1	0	_aImproper Riemann integrals / _cby Ioannis M. Roussos.
250			_a1st.
260			_aBoca Raton, [Florida] : _bCRC, Taylor & Francis Group, _c2014.
300			_axiv, 675 p . ; _c23 cm
336			_atext _2rdacontent
337			_aunmediated _2rdamedia
338			_avolume _2rdacarrier
365			_b4995.00 _cRupees
504			_aIncludes bibliographical references (pages 661-664) and index.
505	0		_aMachine 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 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	_aRiemann integral. _939591
653			_aMathematics
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _c1 _e23 _n0
999			_c613935 _d613935