© 2018

Complex Analysis with Applications


Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Nakhlé H. Asmar, Loukas Grafakos
    Pages 1-94
  3. Nakhlé H. Asmar, Loukas Grafakos
    Pages 95-138
  4. Nakhlé H. Asmar, Loukas Grafakos
    Pages 139-226
  5. Nakhlé H. Asmar, Loukas Grafakos
    Pages 227-291
  6. Nakhlé H. Asmar, Loukas Grafakos
    Pages 293-365
  7. Nakhlé H. Asmar, Loukas Grafakos
    Pages 367-402
  8. Nakhlé H. Asmar, Loukas Grafakos
    Pages 403-482
  9. Back Matter
    Pages 483-494

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.


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

Authors and affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of MathematicsUniversity of MissouriColumbiaUSA

About the authors

​Nakhlé H. Asmar is Professor of Mathematics at the University of Missouri, Columbia.

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
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-94062-5
  • Softcover ISBN 978-3-030-06788-5
  • eBook ISBN 978-3-319-94063-2
  • 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
  • Buy this book on publisher's site


“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)