Complex Analysis with Applications
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Beschreibung
This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences. The overall aim in designing this text is to accommodate students of different mathematical backgrounds and to achieve a balance between presentations of rigorous mathematical proofs and applications.
The text is adapted to enable maximum flexibility to instructors and to students who may also choose to progress through the material outside of coursework. Detailed examples may be covered in one course, giving the instructor the option to choose those that are best suited for discussion. Examples showcase a variety of problems with completely worked out solutions, assisting students in working through the exercises. The numerous exercises vary in difficulty from simple applications of formulas to more advanced project-type problems. Detailed hints accompany the more challenging problems. Multi-part exercises may be assigned to individual students, to groups as projects, or serve as further illustrations for the instructor. Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results. Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website. Additional solutions for instructors’ use may be obtained by contacting the authors directly.This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences. The overall aim in designing this text is to accommodate students of different mathematical backgrounds and to achieve a balance between presentations of rigorous mathematical proofs and applications.
The text is adapted to enable maximum flexibility to instructors and to students who may also choose to progress through the material outside of coursework. Detailed examples may be covered in one course, giving the instructor the option to choose those that are best suited for discussion. Examples showcase a variety of problems with completely worked out solutions, assisting students in working through the exercises. The numerous exercises vary in difficulty from simple applications of formulas to more advanced project-type problems. Detailed hints accompany the more challenging problems. Multi-part exercises may be assigned to individual students, to groups as projects, or serve as further illustrations for the instructor. Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results. Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website. Additional solutions for instructors’ use may be obtained by contacting the authors directly.
Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website; Instructors contact the authors for a full solutions manual Includes a plethora of worked examples and exercises with varying degrees of difficulty Designed for flexible use by instructors and students Numerous graphics help illustrate even the most abstract concepts Includes supplementary material: sn.pub/extras
Autor*in
Nakhlé H. Asmar
Themen in »Complex Analysis with Applications«
complex analysis textbook adoption undergraduate text complex analysis applications complex analysis maximum modulus principle Laplace equation conformal mapping composed mapping complex plane polar form Cauchy-Riemann equations contours in the complex plane Cauchy integral theorem Cauchy-Goursat theorem Cauchy residue theorem Schwarz lemma
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“The book is a clear and rigorous introduction to complex analysis and its applications in applied mathematics, engineering and physics. … Each section of the book contains a great number of examples and exercises.” (Dorina Raducanu, zbMATH 1409.30001, 2019)
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