Calculus with Complex Numbers

Calculus with Complex Numbers



This text is a practical course in complex calculus that covers the applications, but does not assume the full rigour of a real analysis background. Topics covered include algebraic and geometric aspects of complex numbers, differentiation, contour integration, evaluation of finite and infinite real integrals, summation of series and the fundamental theorm of algebra. The Residue Theorem for evaluatting complex integrals is presented in such a way that those wishing to study the subject at a deeper level should not need to unlearn anything presented here. A working knowledge of real calculus is assumed as is an acquaintance with complex numbers. This book is accessible to a any student who has studied calculus at upper school level and will be of interest to undergraduate students of applied mathematics, physical sciences and engineering.