11 Best Books On Complex Analysis

BookSummaryClub Blog 11 Best Books On Complex Analysis

Are you interested in complex analysis- a strange but beautiful subject? Do you need good books to expand your knowledge of complex analysis? If yes, then you’re reading the right article. Complex analysis is the learning of complex numbers with their properties, manipulations, and derivatives 

It is a division of mathematics that works with various mathematical properties of complex variables. Complex analysis has numerous applications in economics, engineering, and physics. To the layperson, it is a subject that involves calculus and uses both imaginary and real numbers. 

Getting the right books on complex analysis can be challenging, but we’ve got you covered. This article comprises the best books on complex analysis; they will help you understand complex analysis better and are highly recommended.

Recommended Books On Complex Analysis

Complex analysis is challenging to study because it requires thinking in three dimensions, but it is fun to learn as it is easy to visualize. Check out the compiled list of good books on complex analysis.

1. A Friendly Approach To Complex Analysis By Sara Maad Sasane, Amol Sasane.

Friendly Approach To Complex Analysis, A
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Friendly Approach To Complex Analysis, A
  • Sasane, Sara Maad (Author)
  • English (Publication Language)
  • 288 Pages – 12/24/2013 (Publication Date) – Wspc (Publisher)

This visual complex analysis book comprises a concise, straightforward, yet challenging course in complex analysis, especially for students who have studied calculus in numerous variables but have not encountered complex analysis.

The primary aim of this book is to enlighten undergraduate students on complex analysis with minimal prerequisites; it is relevant and useful for engineering students and students in joint programs involving mathematics. 

This book’s core content is on the three central pillars of complex analysis, which are- the Cauchy integral theorem, Taylor and Laurent series expansion, and the Cauchy Riemann equations.

Each section of this book comprises different problems, not entirely drill exercises but one that will emphasize the fundamental concepts of complex analysis. 

This book comes with comprehensive solutions to all the activities at the end of the book, which is perfect for self-paced study. This book is written in English and has a total page of 288.

2. Real And Complex Analysis – Volume 1: By Rajnikant Sinha.

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Real and Complex Analysis: Volume 1
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Real and Complex Analysis: Volume 1
  • Hardcover Book
  • Sinha, Rajnikant (Author)
  • English (Publication Language)
  • 646 Pages – 11/15/2018 (Publication Date) – Springer (Publisher)

With a total of 645 pages, this book is an introduction to Lebesgue measure and measure theory, and it’s intended for students in the engineering and mathematical field. It shows where and how the Reisz representation hypothesis works to construct the Lebesgue measure.

This book is in three chapters, and each chapter discusses the following;

  • Measurable and Exponential Functions
  • Fourier Transforms
  • Riesz Representation Theorem
  • Riesz-Fischer Theorem
  • Fubuni Theorem
  • Lebesgue and Borel Measure 
  • Vitali-Caratheodory Theorem

This book also covers the vital analysis needed for developing the concepts thoroughly with adequate detail, learning functional analysis, and prior information on the basics of advanced calculus. 

Furthermore, it includes solutions to extensive exercise that comes with each concept; it also examines some useful theorems in the world of complex and real analysis, and most of them are the works of renowned mathematicians of the 19th & 20th centuries, respectively. 

3. Complex Analysis By Theodore W. Gamelin. 489 Pages.

Complex Analysis (Undergraduate Texts in Mathematics)
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Complex Analysis (Undergraduate Texts in Mathematics)
  • Used Book in Good Condition
  • Gamelin, Theodore W. (Author)
  • English (Publication Language)
  • 498 Pages – 05/18/2001 (Publication Date) – Springer (Publisher)

This book on complex analysis by Gamelin is one of the most well-known books for expanding your knowledge of complex analysis. It is a valuable resource for those interested in complex function theory and complex analysis.  

Written by a skilled mathematician, this remarkable book provides a detailed overview of working with and understanding several complex variables and functions. This well-written book covers Cauchy’s theorem, power series, residue calculus, and holomorphic functions.

This book further discusses the various applications of complex analysis in engineering and physics. It comes with several diagrams and examples, etc. Complex analysis by Theodore W. Gamelin is perfect for beginners, students, or expert mathematicians seeking to enhance their knowledge in the field. 

4. Complex Analysis By Tristan Needham.

Visual Complex Analysis
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Visual Complex Analysis
  • Needham, Tristan (Author)
  • English (Publication Language)
  • 616 Pages – 02/18/1999 (Publication Date) – Clarendon Press (Publisher)

It has a total of 616 pages. This book is a complete guide to complex analysis. Analytic continuation, conformal mappings, hyperbolic functions, and linear transformations are explained in detail in this well-written book.

Written in an easy-to-understand method, this book by Tristan Needham contains intriguing examples to help illustrate the concepts better; it also offers numerous illustrations, diagrams, and practice problems to help beginners grasp the idea of complex analysis better. 

If you want to improve your skills or start in complex analysis, then this book is your best bet. Additionally, it comprises helpful appendices that offer additional information for students or experts looking to delve further into complex analysis.

5. Complex Analysis By Ian Stewart & David Tall – Second Edition. 402 Pages.

Complex Analysis
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Complex Analysis
  • Stewart, Ian (Author)
  • English (Publication Language)
  • 402 Pages – 10/11/2018 (Publication Date) – Cambridge University Press (Publisher)

This book is perfect for students and experts looking for an in-depth and rigorous outline of complex analysis. This rigorous, complex analysis book is a broadly spread and extremely acclaimed work accepted by students and mathematicians alike. 

It offers an intuitive approach to complex analysis, emphasizing mathematical objects and a visual understanding of complex concepts.

It also covers all the significant facets of complex analysis, including analytic functions, power series, and conformal mapping. The author carefully weaves the theory and practice throughout this book, demonstrating how string visual analysis can illuminate complex topics.

This book features numerous examples and exercises with answer sites that can help readers understand complex analysis; this book is perfect for those seeking to understand the enthralling branch of mathematics.

6. Foundations Of Complex Analysis. By S. Ponnusamy.

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Foundations of Complex Analysis
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Foundations of Complex Analysis
  • Ponnusamy, S. (Author)
  • English (Publication Language)
  • 476 Pages – Narosa Pub House (Publisher)

If you want to read and understand complex analysis without the help of anyone, then this book is just for you. It covers numerous and exciting topics like;

  • Limit, Functions, And Continuity
  • Complex Integration
  • Liouvilles Theorem, Maximum Principle, And Schwarz’s Lemma
  • Complex Numbers
  • Power Series And Analytic Functions
  • Mobius Transformations And Conformal Mappings
  • Calculus Of Residues
  • Classification Of Singularities
  • Mapping Theorems
  • Evaluation Of Certain Integrals
  • Representations For Entire & Meromorphic Functions
  • Analytic Continuation

7. Complex Analysis By E.M Stein, R Shakarchi.

Complex Analysis
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Complex Analysis
  • Amazon Kindle Edition
  • Stein, Elias M. (Author)
  • English (Publication Language)
  • 398 Pages – 04/22/2010 (Publication Date) – Princeton University Press (Publisher)

This book is an excellent book by one of the most well-known mathematicians worldwide. This book begins the intricate number system with the easy idea of extending an initially given function for actual values of arguments to the defined one when the argument is complex. The following topics are what you’ll see in this book;

  • Cauchy Theorems
  • Residues
  • The Major Properties Of Holomorphic Functions
  • Argument Principle
  • Contour Integrals
  • Analytic Continuation And Many More

This complex analysis book is helpful for individuals eager to learn for their area of expertise, e.g., mathematics, engineering, or physics.

8. Schaum’s Outline Of Complex Variables By Dennis Spellman, Murray R. Spiegel, John J. Schiller, Seymour Lipschutz.

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Schaum's Outlines: Complex Variables (With an Introduction to Conformal Mapping and Its Applications)
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Schaum’s Outlines: Complex Variables (With an Introduction to Conformal Mapping and Its Applications)
  • Spiegel,Murray (Author)
  • English (Publication Language)
  • 313 Pages – 07/23/1964 (Publication Date) – McGraw-Hill (Publisher)

The beginning of every chapter in this book explains all the theorems, formulas, and propositions together with every related definition. It also contains numerous examples to help you understand the subject, making it a unique book. 

This book is perfect for all college-level students who want to study complex analysis. Graduate students can also benefit from this book if they have comprehensive exams to write on complex analysis.

9. Complex Variables And Applications By James Ward Brown & Ruel V Churchill.

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Complex Variables and Applications (Brown and Churchill)
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Complex Variables and Applications (Brown and Churchill)
  • Used Book in Good Condition
  • Hardcover Book
  • Brown, James Ward (Author)
  • English (Publication Language)
  • 480 Pages – 09/03/2013 (Publication Date) – McGraw Hill (Publisher)

If you want to understand the basics of complex analysis or start a doctoral program in Math, this book is a great place to start. This book will broaden your knowledge of complex analysis while studying it. 

These experienced authors have carefully used a modern approach to explain the calculus of complex analysis concisely and distinctly.

10.  Introductory Complex Analysis By Richard A. Silverman. 400 Pages.

Introductory Complex Analysis (Dover Books on Mathematics)
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Introductory Complex Analysis (Dover Books on Mathematics)
  • Richard A. Silverman (Author)
  • English (Publication Language)
  • 400 Pages – 05/01/1984 (Publication Date) – Dover Publications (Publisher)

This book on complex analysis explains complex numbers most beautifully. Its powers, roots, and geometric representation are discussed in detail, along with complex sequences and functions. Below are the numerous topics in this book;

  • Mobius Transformations
  • Continuity And Limits
  • Rational Fractions And Polynomials
  • Power Series
  • Logarithms And Exponentials
  • Cauchy Theorem & The Complex Integrals
  • Differentiation Of Analytic Functions
  • Singular Points And Laurent Series
  • Residue Theorem
  • Harmonic Functions
  • Analytic Continuation
  • Conformal Mapping And Many More.

This well-written book by Richard A. Silverman is a necessary book for a one-year graduate course or an undergraduate course in complex analysis.

11. Functions Of One Complex Variable By J B Conway.

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Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11)
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Functions of One Complex Variable (Graduate Texts in Mathematics – Vol 11)
  • Hardcover Book
  • John B Conway (Author)
  • English (Publication Language)
  • 330 Pages – 07/23/1978 (Publication Date) – Springer (Publisher)

This book is a well-written textbook that shows the basic concepts and principles of complex analysis. If you desire a different method to learn complex analysis, this textbook is for you. It helps students, beginners, and experts to consolidate some aspects and notions of the complex analysis theory.

This book is written in English and has a total of 330 pages. Its customer reviews are 4.6 out of 5 stars, and its dimension in hardcover is 6.14 X 0.81 X 9.21 inches. You can purchase this book on Amazon online bookstore.

On A Final Note;

Complex analysis can be quite hard to learn, but with the right resources, you can become an expert in the field. All the complex analysis books in this article are perfect for individuals who want to self-study, beginners who want to explore complex analysis, mathematics, physics & engineering students, and experts who wish to enhance their knowledge and understanding. 

Check out these books from renowned authors, as they provide advanced topics and a vast coverage of complex analysis.

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