Overview
- 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
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (7 chapters)
Keywords
- 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
- trigonometric functions
- harmonic functions
- conformal mappings
- Schwarz-Christoffel transformation
About this book
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.
Reviews
Authors and Affiliations
About the authors
Loukas Grafakos is Professor of Mathematics at the University of Missouri at Columbia. In addition to this present UTM, Professor Grafakos has authored two GTM texts, both in their 3rd editions: Classical Fourier Analysis and Modern Fourier Analysis. Additionally, Professor Grafakos is co-Author of Harmonic and Geometric Analysis, (c) 2015, Birkhäuser.
Bibliographic Information
Book Title: Complex Analysis with Applications
Authors: Nakhlé H. Asmar, Loukas Grafakos
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-94063-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-94062-5Published: 23 October 2018
Softcover ISBN: 978-3-030-06788-5Published: 13 December 2018
eBook ISBN: 978-3-319-94063-2Published: 12 October 2018
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: VIII, 494
Number of Illustrations: 385 b/w illustrations, 4 illustrations in colour
Topics: Functions of a Complex Variable