Calculus with complex numbers

This text is a practical course in complex calculus that covers the applications, but does not assume the full rigor 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 theorem of algebra. The Residue Theorem for evaluating 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 will be of interest to undergraduate students of applied mathematics, physical sciences and engineering. This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering. 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