Complex Analysis: A First Course with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. With a clear and straightforward writing style, concepts are introduced through numerous examples, illustrations, and applications. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section devoted exclusively to the applications of complex analysis to science and engineering, providing students with the opportunity to develop a practical and clear understanding of complex analysis. New and Key Features: Clarity of exposition supported by numerous examples Extensive exercise sets with a mix of computational and conceptual problems Applications to science and engineering throughout the text New and revised problems and exercise sets throughout Portions of the text and examples have been revised or rewritten to clarify or expand upon the topics at hand The Mathematica syntax from the second edition has been updated to coincide with version 8 of the software.