Complex Analysis with Applications

by Nakhlé H. Asmar, Loukas Grafakos

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.

Genres: Mathematics

502 pages, Hardcover

Published October 23, 2018

Reviews

[Jesús Rubio · Rating 5 out of 5]

I've read many books on complex analysis/variables; Ahlfors, Zill & Shanahan, Stein & Shakarchi, the one by Schaum, Greene & Krantz, Marsden & Hoffman, Tristan Needham, etc...

And this is the best (at least for an introductory level), i can not believe how good is this book by Asmar and Grafakos, please read this one. Furthermore in springer's web you can find a solutions manual to every other odd problem.

It's just a meatter of time for this book to become a classic

[JRA · Rating 4 out of 5]

I'm almost done with the book:

The book starts very slow and from the very basic of complex numbers; basic algebraic properties (no with abstract algebra, but just mentioning that is a field a vector space over R and just that), polar coordinates, etc. But is very rigorous, at the beginning is very easy book but when you get at the end of chapter 3 to and on you will see that the book gets difficult.

It has a LOT of examples and problems, just an absurd amount of problems, way more than you can cover in an undergraduate class. But a lot of examples and problem are very insightful.

You can think of this book as a very rigorous, topologycal, increasing in difficult introduction to complex analysis. Also the applications come at the 2 last chapter (maybe you can consider application the chapter 5 on residues).

I'm not giving 5 stars because the book has typos, it starts so slowly and easy and out of nowhere the book gets hard and some problems feels like unrelated to the book content lol.