Linear and Complex Analysis for Applications

This book provides an integrated approach to linear algebra and complex analysis, making it suitable for students in engineering and applied mathematics. Linear and Complex Analysis for Applications unifies various topics while showcasing their relevance.

This book develops an understanding of sophisticated tools by using them, focusing on complex variable theory. The first three chapters and selected topics create a cohesive course that should appeal to faculty seeking an integrated treatment of linear algebra and complex analysis, along with applications and a review of vector analysis. Linear and Complex Analysis for Applications aims to unify various aspects of mathematical analysis in an engaging manner, offering a diverse and unusual collection of applications to other fields of mathematics, physics, and engineering.

The book is a product of the author's teaching experiences, research in complex analysis in several variables, and numerous discussions with colleagues and friends. It has three primary goals: to equip students in engineering or applied mathematics with the necessary linear analysis and complex variable theory for advanced work, to unify many distinct and seemingly isolated topics, and to present mathematics as both interesting and useful. This is achieved by juxtaposing examples with theorems to illustrate the concepts.

To realize these goals, the text begins with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III, introducing new material to enhance students' skills in computation and theory. It includes infinite-dimensional examples arising from elementary calculus and differential equations, and computes line and surface integrals using both classical vector analysis and differential forms. The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, with a unifying theme of linear systems, and features over 450 exercises.