This book provides a comprehensive introduction to complex variable theory and applications to current engineering problems and is designed to make the basics of the subject more accessible to readers who have little desire to wade severity axiomatic approach. Modeled after standard calculus books - both at the level of exposition and layout - it incorporates all the physical applications, so the mathematical methodology appears less sterile to engineers. This makes frequent use of analogies from elementary calculus or algebra to introduce complex concepts, includes fully worked examples, and provides a dual heuristic / analytic discussion of all topics. Complex Integration. MATLAB ToolBox for Visualization of Conformal Maps. Features coverage of Julia Sets; modern exposition of the use of complex numbers in linear analysis (eg, AC circuits, kinematics, signal processing); applications of complex algebra in celestial mechanics and gear kinematics; and an introduction to Cauchy integrals and Sokhotskyi-Plemeij formula. For mathematicians and engineers interested in Complex Analysis and Mathematical Physics.