Improper Riemann Integrals

Ioannis Markos Roussos

December 16, 2013 by Chapman and Hall/CRC
Reference - 689 Pages - 36 B/W Illustrations
ISBN 9781466588073 - CAT# K20366


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  • Describes various methods from advanced calculus and real and complex analysis for computing improper integrals
  • Provides the necessary theorems and results
  • Offers justification for many steps by using the tools of advanced analysis, a feature often omitted from other books
  • Contains detailed examples that illustrate the tools for checking convergence of improper integrals and evaluating their exact value when possible
  • Presents many of the same examples in different ways, highlighting the interconnection among topics, how a problem can be viewed in various contexts, and how different methods can solve the same problem
  • Includes problems in every section, several projects and applications, and an extensive bibliography at the back of the book
  • Lists all the major integrals and finite and infinite sums computed in the text


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.