Complex Analysis with Applications to Flows and Fields

This book presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. It gives the necessary mathematical background and physical principles to build models for technological and scientific purposes, showing how to formulate problems, justify the solutions, and interpret the results. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It also provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references.