7+ Best Complex Analysis Books [2023 Review]

Best reference books of Complex Analysis: If you are looking for the top complex analysis books, then you are right place. As I have over 16 years of experience in Complex Analysis, it makes me easier to decide the best books on complex analysis to buy even if you are a beginner on this topic. The top complex analysis books are given as follows:

1. Complex Analysis (Princeton Lectures in Analysis, No. 2)

Author: E M Stein, R Shakarchi

The author E M Stein is one of the most famous mathematicians in the world. This book on complex analysis by Stein Shakarchi is an excellent book.

The book starts the complex number system with the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. The following topics are covered in the book: the main properties of holomorphic functions, Cauchy theorems, contour integrals, residues, analytic continuation, and the argument principle, etc. This book is very useful for those who are eager to learn complex analysis for their own area of expertise (ex. Physics, Engineering, etc other than Maths).

Product Details:

  • Publisher ‏ : ‎ Princeton University Press; Illustrated edition (April 27, 2003)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 400 pages
  • ISBN-13 ‏ : ‎ 978-0691113852
  • Item Weight ‏ : ‎ 1.56 pounds
  • Dimensions ‏ : ‎ 6.5 x 1.18 x 9.36 inches
  • Customer Reviews: 4.5 out of 5 stars (88 ratings)   

2. Introductory Complex Analysis (Dover Books on Mathematics)

Author: Richard A. Silverman

The book starts with defining complex numbers in a beautiful way; and then their geometric representation, powers and roots of complex numbers are discussed along with complex functions and sequences. The topics below are covered and clearly explained:

limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations, exponentials and logarithms, complex integrals and the Cauchy theorem, complex series and uniform convergence, power series, Laurent series and singular points, residue theorem, harmonic functions, conformal mapping, analytic continuation, and many more.

The complex analysis book by Silverman is one of the essential books for an undergraduate course or a one-year graduate course in complex analysis.

Product Details:

  • Publisher ‏ : ‎ Dover Publications (May 1, 1984)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 400 pages
  • ISBN-13 ‏ : ‎ 978-0486646862
  • Item Weight ‏ : ‎ 14.5 ounces
  • Dimensions ‏ : ‎ 5.38 x 0.78 x 8.43 inches
  • Customer Reviews: 4.5 out of 5 stars (61 ratings)   

3. Schaum’s Outline of Complex Variables

Author: Murray R. Spiegel, Seymour Lipschutz, John J. Schiller, Dennis Spellman

At the beginning of each chapter, the book quickly explains all the formulas, propositions, and theorems together with all the related definitions. After that, it contains many solved examples which help you to grasp the subject. The step-by-step solution will touch your mind and makes it a unique book in its own way.

Schaum’s Outline of Complex Variables is highly recommended for college-level students studying complex analysis. Graduate students can be benefitted to pass the comprehensive exams on complex analysis.

Product Details:

  • ASIN ‏ : ‎ 0071615695
  • Publisher ‏ : ‎ McGraw Hill; 2nd edition (June 10, 2009)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 384 pages
  • ISBN-13 ‏ : ‎ 978-0071615693
  • Item Weight ‏ : ‎ 1.91 pounds
  • Dimensions ‏ : ‎ 8.1 x 0.7 x 10.9 inches
  • Customer Reviews: 4.5 out of 5 stars (159 ratings)   

4. Complex Variables and Applications

Author: James Ward Brown and Ruel V Churchill

To build a basic idea of complex analysis, this book by Brown and Churchill is very useful. If you want to enter a doctoral program in Mathematics, this book can help you to clear the interview. This is because it can help you to think about the subject while studying the book. The authors have explained the calculus of complex analysis very clearly and neatly.

Product Details:

  • Publisher ‏ : ‎ MC GRAW HILL INDIA; 8th edition (January 1, 2014)
  • Language ‏ : ‎ English
  • ISBN-13 ‏ : ‎ 978-9339205157
  • Item Weight ‏ : ‎ 1.14 pounds
  • Dimensions ‏ : ‎ 15.39 x 1.61 x 22.8 inches
  • Customer Reviews: 4.3 out of 5 stars (220 ratings)   

5. Foundations Of Complex Analysis

Author: S. Ponnusamy

If you like to read complex analyis, and want to understand without help, this book by S. Ponnusamy is really made for you. For this reason, the book should have got a 5-star rating. The topics discussed here are the following:

  1. complex numbers
  2. Functions, Limit and Continuity
  3. Analytic Functions and Power Series
  4. Complex Integration
  5. Conformal Mappings and Mobius Transformations
  6. Maximum Principle, Schwarz’s Lemma, and Liouville’s Theorem
  7. Classification of Singularities
  8. Calculus of Residues
  9. Evaluation of certain Integrals
  10. Analytic Continuation
  11. Representations for Meromorphic and Entire Functions
  12. Mapping Theorems

Product Details:

  • Language ‏ : ‎ English
  • ISBN-13 ‏ : ‎ 978-8173196294
  • Item Weight ‏ : ‎ 1.76 pounds
  • Dimensions ‏ : ‎ 7.87 x 5.51 x 1.57 inches
  • Customer Reviews: 4.2 out of 5 stars (123 ratings)   

6. Functions of One Complex Variable

Author: J B Conway

Functions of One Complex Variable Vol. I is a well-written textbook that presents basic principles and concepts of Complex Analysis. If you want to learn the subject differently, then this textbook helps a lot the reader to consolidate some notions and aspects of the theory.

Product Details:

  • Publisher ‏ : ‎ Springer; 2nd edition (January 1, 1978)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 330 pages
  • ISBN-13 ‏ : ‎ 978-0387903286
  • Item Weight ‏ : ‎ 3.17 pounds
  • Dimensions ‏ : ‎ 6.14 x 0.81 x 9.21 inches
  • Customer Reviews: 4.6 out of 5 stars (57 ratings)   

7. Complex Analysis by Ahlfors

Author: Ahlfors

The book can be considered as a “how to think like a Mathematician” textbook.

Complex Analysis by Ahlfors deals with the following topics: complex functions, complex Integration, conformal mapping, analytic functions, and many more. One of the main theorems in complex analysis is Cauchy’s theorem and it is explained very extensively. The book is recommended for graduate-level students or undergraduate students who want to learn the theory from their heart.

Product Details:

  • ASIN ‏ : ‎ 1259064824
  • Publisher ‏ : ‎ MC GRAW HILL INDIA; 3rd edition (January 1, 1979)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 348 pages
  • ISBN-13 ‏ : ‎ 978-1259064821
  • Item Weight ‏ : ‎ 12 ounces
  • Dimensions ‏ : ‎ 15.31 x 1.3 x 22.8 inches
  • Customer Reviews: 4.4 out of 5 stars (238 ratings)   

8. Real and Complex Analysis by Rudin

Author: Walter Rudin
Real and Complex Analysis by Rudin

The way topics are covered in the Real and Complex Analysis text by Rudin is unmatched. After finishing the book, you can prepare for other graduate texts and read the literature. The unique feature of the book is that it includes two distinct topics of “complex analysis” and “real analysis” in a single volume.

It will be a great choice if you would like to acquire a fairly advanced level of knowledge in both real and complex analysis.

Product Details:

  • Publisher ‏ : ‎ MC GRAW HILL INDIA; 3rd edition (January 1, 1987)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 483 pages
  • ISBN-13 ‏ : ‎ 978-0070619876
  • Item Weight ‏ : ‎ 14.1 ounces
  • Dimensions ‏ : ‎ 7.99 x 10 x 1.85 inches
  • Customer Reviews: 4.4 out of 5 stars (145 ratings)   

FAQs

Q: What are the best complex analysis books?

Answer: The list of best complex analysis books is given as follows:

1. Complex Analysis (Princeton Lectures in Analysis, No. 2) [by E M Stein, R Shakarchi]

2. Introductory Complex Analysis (Dover Books on Mathematics) [Author: Richard A. Silverman]

3. Schaum’s Outline of Complex Variables

4. Complex Variables and Applications, by Churchill & Brown

5. Foundations Of Complex Analysis, by S. Ponnusamy

6. Functions of One Complex Variable, by J B Conway

7. Complex Analysis by Ahlfors

8. Real and Complex Analysis [by Walter Rudin]

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