Improper Riemann integrals
By: Ioannis M. Roussos, Hamline University, Saint Paul, Minnesota, USA
Publisher: CRC, Taylor & Francis Group
Published: 2014
Place of publication: Boca Raton, [Florida]
Language: eng
Number of pages: 675
ISBN-13: 9781466588073
Copyright date: 2014
Subjects: Riemann integral
Notes: Includes bibliographical references (pages 661-664) and index.
Table of contents: title: Machine generated contents note: 1.Improper Riemann Integrals; title: 1.1.Definitions and Examples; title: 1.1.1.Applications; title: 1.2.Cauchy Principal Value; title: 1.3.Some Criteria of Existence; title: 2.Real Analysis Techniques; title: 2.1.Calculus Techniques; title: 2.1.1.Applications; title: 2.2.Integrals Dependent on Parameters; title: 2.3.Commuting Limits with Integrals and Derivatives; title: 2.3.1.Commuting Limits and Integrals; title: 2.3.2.Commuting Limits and Derivatives; title: 2.4.Double Integral Technique; title: 2.5.Frullani Integrals; title: 2.6.The Real Gamma and Beta Functions; title: 2.6.1.The Gamma Function; title: 2.6.2.The Beta Function; title: 2.6.3.Applications; title: 2.7.A Brief Overview of Laplace Transform; title: 2.7.1.Laplace Transform; title: 2.7.2.Inverse Laplace Transform; title: 2.7.3.Applications; title: 3.Complex Analysis Techniques; title: 3.1.Basics of Complex Variables; title: 3.1.1.Basic Definitions and Operations; title: 3.1.2.Representations and Roots of Complex Numbers; title: 3.1.3.Square Roots without De Moivre; title: 3.2.Power Series; title: a Quick Review; title: 3.3.Limits, Continuity and Derivatives; title: 3.4.Line Integrals in the Complex Plane; title: 3.5.Cauchy-Goursat Theorem and Consequences; title: 3.5.1.Complex Preliminaries and Notation; title: 3.5.2.Cauchy-Goursat Theorem; title: 3.5.3.Complex Logarithm; title: 3.5.4.Complex Power Functions; title: 3.5.5.Properties of Complex Logarithms and Powers; title: 3.5.6.Consequence; title: 3.5.7.Cauchy Integral Formula; title: 3.5.8.Appendix; title: 3.6.Roots, Singularities, Residues; title: 3.6.1.Definitions, Laurent Expansion and Examples; title: 3.6.2.Five Ways to Evaluate Residues; title: 3.7.Contour Integration and Integrals; title: 3.7.1.Residue Theorem and Examples; title: 3.7.2.Contour Integration and Improper Real Integrals; title: 3.7.3.Infinite Isolated Singularities and Integrals; title: 3.7.4.Infinite Isolated Singularities and Series; title: 3.7.5.Fourier Type Integrals; title: 3.7.6.Rules and Properties of the Fourier Transform; title: 3.7.7.Applications; title: 3.7.8.The Fourier Transform with Complex Argument; title: 3.7.9.Improper Integrals and Logarithms; title: 3.7.10.Application to Inverse Laplace Transform; title: 3.8.Definite Integrals with Sines and Cosines; title: 3.8.1.Rational Functions of Sines and Cosines; title: 3.8.2.Other Techniques with Sines and Cosines; title: 3.8.3.Appendix; title: 4.List of Non-elementary Integrals and Sums in Text; title: 4.1.List of Non-elementary Integrals; title: 4.2.List of Non-elementary Sums.