Complex Analysis with Applications to Flows and Fields

ISBN-13: 9781420071184 / Angielski / Twarda / 2010 / 1030 str.

Luis Manuel Braga de Costa Campos

Opis

Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references. The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples. This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.

With a focus on interdisciplinary areas, Complex Functions with Applications to Flows and Fields provides an overview of the mathematical modeling of physical phenomena and engineering processes. The author, considered one of Europe’s leading applied mathematicians, presents a unified treatment of complex functions. This volume emphasizes how similar methods can be applied to analogous problems in different areas with specific interpretations. Each chapter includes problems with solutions as well as illustrative examples and practical applications. Accessible for all readers, the text progresses from an undergraduate to a post-graduate level, offering deeper insight into key topics.

Spis treści

Complex Domain: Circuits and Stability. Integrals and Residues: Flows and Gravity. Power Series: Electricity and Magnetism. Conformal Mapping: Heat and Aerodynamics. Bibliography. Index.

O autorze

Luis Manuel Braga da Costa Campos is the director of the Center for Aeronautical and Space Science and Technology at Lisbon Technical University in Portugal.