TY  - BOOK
AU  - Roussos,Ioannis Markos
TI  - Improper Riemann integrals
SN  - 9781032032054 (pbk.)
U1  - 515.43 23
PY  - 2014///
CY  - Boca Raton, [Florida]
PB  - CRC, Taylor & Francis Group
KW  - Riemann integral
KW  - Mathematics
N1  - Includes bibliographical references (pages 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 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
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