Complex Integration

The book is the result of nine years of providing solutions to difficult calculus problems on forums such as Math Stack Exchange or the author's website, residuetheorem.com; this book details to the enthusiastic mathematics undergraduate, or the physics or engineering graduate student, the art and science of evaluating difficult integrals, sums, and products. While there are several books on the market that provide tutorials on this subject, this book proposes techniques that mainly use complex integration and are quite different from those in the existing texts.What is interesting is that many of the integrals and sums are not usually considered for evaluation using complex integration. Such techniques, ostensibly taught in a course in Complex Analysis to undergraduate students having had two semesters of calculus, are limited to a very small set of problems. Few practitioners consider complex integration as a tool to compute difficult integrals; rather, the existing texts in this space focus on real methods. Accordingly, the book is an eye-opening experience for computation enthusiasts used to relying on clever substitutions and transformations to evaluate integrals and sums.