# Basic Complex Analysis by by J. E. Marsden and M.J. Hoffman

• Analysis
• Greg Bernhardt
In summary, "Basic Complex Analysis" by J. E. Marsden and M.J. Hoffman is a highly recommended textbook for those studying Complex Analysis. It presents the topics in a clear and accessible manner, making it a great second book for beginners in the subject. The book covers analytic functions, Cauchy's theorem, series representation of analytic functions, calculus of residues, conformal mappings, and more. It also includes exercises and answers for further practice.

## For those who have used this book

• ### Strongly don't Recommend

• Total voters
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[LIST]
[*] Analytic Functions
[LIST]
[*] Introduction to Complex Numbers
[*] Properties of Complex Numbers
[*] Some Elementary Functions
[*] Continuous Functions
[*] Basic Properties of Analytic Functions
[*] Differentiation of the Elementary Functions
[/LIST]
[*] Cauchy's Theorem
[LIST]
[*] Contour Integrals
[*] Cauchy's Theorem—A First Look
[*] A Closer Look at Cauchy's Theorem
[*] Cauchy's Integral Formula
[*] Maximum Modulus Theorem and Harmonic Functions
[/LIST]
[*] Series Representation of Analytic Functions
[LIST]
[*] Convergent Series of Analytic Functions
[*] Power Series and Taylor's Theorem
[*] Laurent Series and Classification of Singularities
[/LIST]
[*] Calculus of Residues
[LIST]
[*] Calculation of Residues
[*] Residue Theorem
[*] Evaluation of Definite Integrals
[*] Evaluation of Infinite Series and Partial-Fraction Expansions
[/LIST]
[*] Conformal Mappings
[LIST]
[*] Basic Theory of Conformal Mappings
[*] Fractional Linear and Schwarz-Christoffel Transformations
[*] Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
[/LIST]
[*] Further Development of the Theory
[LIST]
[*] Analytic Continuation and Elementary Riemann Surfaces
[*] Rouche's Theorem and Principle of the Argument
[*] Mapping Properties of Analytic Functions
[/LIST]
[*] Asymptotic Methods
[LIST]
[*] Infinite Products and the Gamma Function
[*] Asymptotic Expansions and the Method of Steepest Descent
[*] Stirling's Formula and Bessel Functions
[/LIST]
[*] Laplace Transform and Applications
[LIST]
[*] Basic Properties of Laplace Transforms
[*] Complex Inversion Formula
[*] Application of Laplace Transforms to Ordinary Differential Equations
[/LIST]
[*] Index
[/LIST]

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I've tried over the last 5 years, many intro Complex Analysis textbooks and this one is by far the best one I've used. It's not overly-complicated, not too many proofs, and is a pleasant read compared to other textbooks which are difficult to follow. It presents the topics in a very accessible way that I believe the student can follow without difficulty.

I would highly recommend this text as a second book for anyone taking the subject for the first time. I use my often.

## 1. What is the purpose of "Basic Complex Analysis" by J.E. Marsden and M.J. Hoffman?

The purpose of this book is to introduce readers to the fundamentals of complex analysis, which is a branch of mathematics that deals with the study of functions of complex variables. It covers topics such as complex numbers, analytic functions, and contour integration.

## 2. Is this book suitable for beginners in complex analysis?

Yes, this book is designed for students who have a basic understanding of calculus and linear algebra. It starts with the basics of complex numbers and gradually builds up to more advanced topics, making it suitable for beginners.

## 3. How is this book different from other textbooks on complex analysis?

This book is known for its clear and concise writing style, making it accessible for students with different levels of mathematical background. It also includes numerous examples and exercises to help readers understand and apply the concepts. Additionally, it covers topics that are often omitted in other textbooks, such as the Cauchy-Riemann equations and conformal mapping.

## 4. Can this book be used for self-study?

Yes, this book can be used for self-study as it is well-structured and includes solutions to selected exercises. However, it is recommended to have a basic knowledge of calculus and linear algebra before attempting to study complex analysis on your own.

## 5. Is this book suitable for advanced studies in complex analysis?

While this book covers the fundamentals of complex analysis, it may not be sufficient for advanced studies. It is a good starting point for beginners, but students who wish to pursue advanced topics in complex analysis may need to refer to other textbooks or additional resources.

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