Complex Analysis: A Modern First Course in Function Theory 1st Edition by Jerry R. Muir Jr. (PDF)

Description

A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subjectWritten with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem.Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features:Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projectsNumerous figures to illustrate geometric concepts and constructions used in proofsRemarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notesAppendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.

User’s Reviews

Editorial Reviews: Review “The textbook is appropriate for students and can serve as a key reference for anyone interested in learning or reviewing the theory of complex functions of a complex variable.” (Zentralblatt MATH 2016) The textbook is appropriate for students and can serve as a key reference for anyone interested in learning or reviewing the theory of complex functions of a complex variable. From the Inside Flap A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subjectWritten with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projectsNumerous figures to illustrate geometric concepts and constructions used in proofsRemarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notesAppendices on the basics of sets and functions and a handful of useful results from advanced calculusAppropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis. From the Back Cover A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subjectWritten with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projectsNumerous figures to illustrate geometric concepts and constructions used in proofsRemarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notesAppendices on the basics of sets and functions and a handful of useful results from advanced calculusAppropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis. About the Author Jerry R. Muir, Jr., PhD, is Professor of Mathematics at The University of Scranton. He has authored over one dozen research articles in complex-flavored analysis, primarily on geometric function theory in several complex variables. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book has good design and seems to easy other complex varibles textbooks.But some important results in complex variables has left exercise without solutions.(ex. argument principles,,,) It is a little inconvenient.

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