An edition of Improper Riemann integrals
(2014)
Improper Riemann integrals
by Ioannis Markos Roussos
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Book Details
Table of Contents
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.
Edition Notes
Includes bibliographical references (pages 661-664) and index.
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| December 15, 2022 | Edited by MARC Bot | import existing book |
| September 17, 2021 | Edited by ImportBot | import existing book |
| November 14, 2020 | Created by MARC Bot | import new book |