03467cam a2200337 i 450000100090000000300040000900500170001300800410003001000170007102000250008803500130011304000290012608200220015510000440017724500570022125000090027826000650028730000260035233600210037833700250039933800230042436500200044750400670046750523080053465000290284265300160287190600450288794200180293299900190295095201600296917887834OSt20260513142931.0130916t20142014flu      b    001 0 eng    a  2013037630  a9781032032054 (pbk.)  a17887834  aDLCbengcJKRCerdadDLC00223a515.43bROU.I1 aRoussos, Ioannis Markos.eauthor93959010aImproper Riemann integrals /cby Ioannis M. Roussos.  a1st.  aBoca Raton, [Florida] :bCRC, Taylor & Francis Group,c2014.  axiv, 675 p . ;c23 cm  atext2rdacontent  aunmediated2rdamedia  avolume2rdacarrier  b4995.00cRupees  aIncludes bibliographical references (pages 661-664) and index.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. 0aRiemann integral.939591  aMathematics  a7bcbccorignewd1eecipf20gy-gencatlg  2ddcc1e23n0  c613935d613935  00102ddc4070a2b2d2026-02-28eThe Forward Books, 25271 / 05-01-2026.i523730o515.43 ROU.Ip523730r2026-02-28v4995.00w2026-02-28y1z4995.00 Rupees