Improper Riemann Integrals: 1st Edition (Hardback) book cover

Improper Riemann Integrals

1st Edition

By Ioannis Markos Roussos

Chapman and Hall/CRC

689 pages | 36 B/W Illus.

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Hardback: 9781466588073
pub: 2013-12-16
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Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineering problems.

The book contains the necessary background, theorems, and tools, along with two lists of the most important integrals and sums computed in the text. Numerous examples at various levels of difficulty illustrate the concepts and theorems. The book uses powerful tools of real and complex analysis not only to compute the examples and solve the problems but also to justify that the computation methods are legitimate.

Enriched with many examples, applications, and problems, this book helps students acquire a deeper understanding of the subject, preparing them for further study. It shows how to solve the integrals without exclusively relying on tables and computer packages.


"When one wants to calculate an improper Riemann integral one is facing various pitfalls. This is why an enormous amount of examples, exercises, and problems is la raison d’etre of this book, which is devoted to the calculation of improper Riemann integrals. Moreover, the author does his best to make the book as accessible as possible. … I can recommend this book, which shows to students, among other things, the power of ‘elementary techniques.’"

Mathematical Reviews, January 2015

"By collecting a lot of important improper integrals and sums used in various domains, and presenting their calculation in an accessible but rigorous way, the book will be of great use to students in mathematics and related areas and for applied scientists (statisticians, engineers, physicists) as well."

Studia Universitatis Babes-Bolyai Mathematica, 59, 2014

Table of Contents

Improper Riemann Integrals

Definitions and Examples

Cauchy Principal Value

Some Criteria of Existence

Real Analysis Techniques

Calculus Techniques

Integrals Dependent on Parameters

Commuting Limits with Integrals and Derivatives

Double Integral Technique

Frullani Integrals

The Real Gamma and Beta Functions

A Brief Overview of Laplace Transform

Complex Analysis Techniques

Basics of Complex Variables

Power Series, a Quick Review

Limits, Continuity and Derivatives

Line Integrals in the Complex Plane

Cauchy-Goursat Theorem and Consequences

Roots, Singularities, Residues

Contour Integration and Integrals

Definite Integrals with Sines and Cosines

List of Non-Elementary Integrals and Sums in Text

List of Non-Elementary Integrals

List of Non-Elementary Sums



Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
MATHEMATICS / Functional Analysis