Improper Riemann Integrals

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.

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 DerivativesDouble Integral Technique Frullani Integrals The Real Gamma and Beta FunctionsA Brief Overview of Laplace Transform Complex Analysis Techniques Basics of Complex VariablesPower Series, a Quick ReviewLimits, Continuity and Derivatives Line Integrals in the Complex Plane Cauchy-Goursat Theorem and ConsequencesRoots, Singularities, Residues Contour Integration and IntegralsDefinite Integrals with Sines and Cosines List of Non-Elementary Integrals and Sums in Text List of Non-Elementary Integrals List of Non-Elementary Sums Bibliography Index