# Complex Variables and Applications by Brown and Churchill

• Analysis
• micromass
In summary: The author does a great job of integrating these topics together while still making them understandable. Additionally, I found the author's writing style to be both engaging and easy to follow. I would definitely recommend this text to anyone who is looking to gain a better understanding of complex analysis.In summary, Complex Variables and Applications is a great book for those who are looking to dive a little deeper into the subject of complex analysis. It is well-written and easy to follow, and the author does a great job of integrating vector calculus, complex analysis, and integrals/differentials together. I would highly recommend this book to anyone who is looking to gain

## For those who have used this book

• ### Lightly don't Recommend

• Total voters
8
micromass
Staff Emeritus
Homework Helper

Code:
[LIST]
[*] Preface
[*] Complex Numbers
[LIST]
[*] Sums and Products
[*] Basic Algebraic Properties
[*] Further Properties
[*] Vectors and Moduli
[*] Complex Conjugates
[*] Exponential Form
[*] Products and Powers in Exponential Form
[*] Arguments of Products and Quotients
[*] Roots of Complex Numbers
[*] Examples
[*] Regions in the Complex Plane
[/LIST]
[*] Analytic Functions
[LIST]
[*] Functions of a Complex Variable
[*] Mappings
[*] Mappings by the Exponential Function
[*] Limits
[*] Theorems on Limits
[*] Limits Involving the Point at Infinity
[*] Continuity
[*] Derivatives
[*] Differentiation Formulas
[*] Cauchy-Riemann Equations
[*] Sufficient Conditions for Differentiability
[*] Polar Coordinates
[*] Analytic Functions
[*] Examples
[*] Harmonic Functions
[*] Uniquely Determined Analytic Functions
[*] Reflection Principle
[/LIST]
[*] Elementary Functions
[LIST]
[*] The Exponential Function
[*] The Logarithmic Function
[*] Branches and Derivatives of Logarithms
[*] Some Identities Involving Logarithms
[*] Complex Exponents
[*] Trigonometric Functions
[*] Hyperbolic Functions
[*] Inverse Trigonometric and Hyperbolic Functions
[/LIST]
[*] Integrals
[LIST]
[*] Derivatives of Functions w(t)
[*] Definite Integrals of Functions w(t)
[*] Contours
[*] Contour Integrals
[*] Some Examples
[*] Examples with Branch Cuts
[*] Upper Bounds for Moduli of Contour Integrals
[*] Antiderivatives
[*] Proof of the Theorem
[*] Cauchy-Goursat Theorem
[*] Proof of the Theorem
[*] Simply Connected Domains
[*] Multiply Connected Domains
[*] Cauchy Integral Formula
[*] An Extension of the Cauchy Integral Formula
[*] Some Consequences of the Extension
[*] Liouville's Theorem and the Fundamental Theorem of Algebra
[*] Maximum Modulus Principle
[/LIST]
[*] Series
[LIST]
[*] Convergence of Sequences
[*] Convergence of Series
[*] Taylor Series
[*] Proof of Taylor's Theorem
[*] Examples
[*] Laurent Series
[*] Proof of Laurent's Theorem
[*] Examples
[*] Absolute and Uniform Convergence of Power Series
[*] Continuity of Sums of Power Series
[*] Integration and Differentiation of Power Series
[*] Uniqueness of Series Representations
[*] Multiplication and Division of Power Series
[/LIST]
[*] Residues and Poles
[LIST]
[*] Isolated Singular Points
[*] Residues
[*] Cauchy's Residue Theorem
[*] Residue at Infinity
[*] The Three Types of Isolated Singular Points
[*] Residues at Poles
[*] Examples
[*] Zeros of Analytic Functions
[*] Zeros and Poles
[*] Behavior of Functions Near Isolated Singular Points
[/LIST]
[*] Applications of Residues
[LIST]
[*] Evaluation of Improper Integrals
[*] Example
[*] Improper Integrals from Fourier Analysis
[*] Jordan's Lemma
[*] Indented Paths
[*] An Indentation Around a Branch Point
[*] Integration Along a Branch Cut
[*] Definite Integrals Involving Sines and Cosines
[*] Argument Principle
[*] Rouché's Theorem
[*] Inverse Laplace Transforms
[*] Examples
[/LIST]
[*] Mapping by Elementary Functions
[LIST]
[*] Linear Transformations
[*] The Transformation w = 1/z
[*] Mappings by 1/z
[*] Linear Fractional Transformations
[*] An Implicit Form
[*] Mappings of the Upper Half Plane
[*] The Transformation w = sin z
[*] Mappings by z^2 and Branches of z^{1/2}
[*] Square Roots of Polynomials
[*] Riemann Surfaces
[*] Surfaces for Related Functions
[/LIST]
[*] Conformal Mapping
[LIST]
[*] Preservation of Angles
[*] Scale Factors
[*] Local Inverses
[*] Harmonic Conjugates
[*] Transformations of Harmonic Functions
[*] Transformations of Boundary Conditions
[/LIST]
[*] Applications of Conformal Mapping
[LIST]
[*] Steady Temperatures in a Half Plane
[*] A Related Problem
[*] Electrostatic Potential
[*] Potential in a Cylindrical Space
[*] Two-Dimensional Fluid Flow
[*] The Stream Function
[*] Flows Around a Corner and Around a Cylinder
[/LIST]
[*] The Schwarz--Christoffel Transformation
[LIST]
[*] Mapping the Real Axis Onto a Polygon
[*] Schwarz--Christoffel Transformation
[*] Triangles and Rectangles
[*] Degenerate Polygons
[*] Fluid Flow in a Channel Through a Slit
[*] Flow in a Channel With an Offset
[*] Electrostatic Potential About an Edge of a Conducting Plate
[/LIST]
[*] Integral Formulas of the Poisson Type
[LIST]
[*] Poisson Integral Formula
[*] Dirichlet Problem for a Disk
[*] Related Boundary Value Problems
[*] Schwarz Integral Formula
[*] Dirichlet Problem for a Half Plane
[*] Neumann Problems
[/LIST]
[*] Appendixes
[LIST]
[*] Bibliography
[*] Table of Transformations of Regions
[/LIST]
[*] Index
[/LIST]

Last edited by a moderator:
Solid user-friendly intro book on complex variables, sort of a rough equivalent to linear algebra done right.

I'd highly recommend for a physics or chemistry student who wants a better grasp of residues and conformal mappings, but which is not too mathematically intense.

This is a decent introductory book, geared well toward physicists and engineers but rigorous enough to not offend a math-major. It is clearly written and organized, making it decent as a reference book.

However, it doesn't give much insight into the beauty of the subject. This is a common required textbook for intro courses, so I recommend also getting Visual Complex Analysis as an interesting supplementary text.

There is also a solid free textbook here:
http://www.math.uiuc.edu/~r-ash/CV.html

I am familliar with the author's abstract algebra book (which I like), but I have only skimmed parts of this one.

I am familiar with the 5th edition, which I have had for about 20 years. I think it is a reasonable book that covers most of the material many engineers/physicists need for routine applications. By far my favorite sections are those on conformal mapping - the presentation is quite good for applications. In most ways Churchill and Brown is better than the book I had to buy for my complex analysis class (introduction to complex analysis, by Priestley), but I am not wild about the organization of most of the book. Overall I prefer the book by Saff and Snider for an introduction.

I studied the first ten chapters of this book (omitting the final chapters on applications). I used the seventh edition (the eighth edition is now the most current one). I found this text to be ideal for someone (such as myself) who had studied complex analysis a long time ago and wanted to relearn it. The text is almost entirely free of typos and errors, which I find to be important for self-study. The proofs are clear and the examples well-chosen. The exercises are primarily calculations, with a few simple proofs thrown in. This is not a criticism; I found some of the calculations to be challenging. Someone who wants to study more advanced topics in Complex Analysis should consult a second book, such as Lang, Ahlfors or Conway (after studying this text).

## 1. What is the main focus of "Complex Variables and Applications by Brown and Churchill"?

The main focus of this book is to provide a comprehensive introduction to complex analysis, which is a branch of mathematics that studies functions of complex numbers and their properties.

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

Yes, this book is suitable for beginners as it starts with basic concepts and gradually builds upon them. It also includes many examples and exercises to help readers understand the material.

## 3. What topics are covered in this book?

This book covers topics such as complex numbers, analytic functions, contour integration, power series, conformal mapping, and the Cauchy-Riemann equations. It also includes applications in physics, engineering, and other areas of mathematics.

## 4. Are there any online resources available for this book?

Yes, there are online resources available for this book, such as a solutions manual and additional practice problems. These resources can be found on the publisher's website or through a quick internet search.

## 5. Is "Complex Variables and Applications by Brown and Churchill" a popular book in the field of complex analysis?

Yes, this book is considered a classic in the field of complex analysis and is widely used by students and professionals alike. It has been praised for its clear explanations and comprehensive coverage of the subject.

• Science and Math Textbooks
Replies
1
Views
6K
• Science and Math Textbooks
Replies
1
Views
4K
• Science and Math Textbooks
Replies
1
Views
4K
• Science and Math Textbooks
Replies
1
Views
4K
• Science and Math Textbooks
Replies
4
Views
6K
• Science and Math Textbooks
Replies
1
Views
4K
Replies
18
Views
2K
• Science and Math Textbooks
Replies
4
Views
7K
• Science and Math Textbooks
Replies
15
Views
15K
• Science and Math Textbooks
Replies
2
Views
2K