Complex Variables: A Physical Approach with Applications and MATLAB

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $40.24
Usually ships in 1-2 business days
(Save 67%)
Other sellers (Hardcover)
  • All (6) from $40.24   
  • New (4) from $62.59   
  • Used (2) from $40.24   


From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice.

The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, Maple™, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering.

Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences.

Read More Show Less

Product Details

  • ISBN-13: 9781584885801
  • Publisher: Taylor & Francis
  • Publication date: 8/31/2007
  • Series: Textbooks in Mathematics Series, #1
  • Edition description: New Edition
  • Pages: 358
  • Product dimensions: 7.20 (w) x 10.00 (h) x 1.10 (d)

Table of Contents


Complex Arithmetic
Algebraic and Geometric Properties
The Exponential and Applications

Holomorphic Functions
Holomorphic and Harmonic Functions
Real and Complex Line Integrals
Complex Differentiability
The Logarithm

The Cauchy Integral Theorem
Variants of the Cauchy Formula
The Limitations of the Cauchy Formula

The Derivatives of a Holomorphic Function
The Zeros of a Holomorphic Function

Behavior near an Isolated Singularity
Expansion around Singular Points
Examples of Laurent Expansions
The Calculus of Residues
Applications to the Calculation of Integrals
Meromorphic Functions

Counting Zeros and Poles
Local Geometry of Functions
Further Results on Zeros
The Maximum Principle
The Schwarz Lemma

The Idea of a Conformal Mapping
Mappings of the Disc
Linear Fractional Transformations
The Riemann Mapping Theorem
Conformal Mappings of Annuli
A Compendium of Useful Conformal Mappings

Conformal Mapping
The Dirichlet Problem
Physical Examples
Numerical Techniques

Basic Properties of Harmonic Functions
The Mean Value Property
The Poisson Integral Formula

Introductory Remarks
Fourier Series
The Fourier Transform
The Laplace Transform
A Table of Laplace Transforms
The z-Transform

Fourier Methods

Introductory Remarks
The Software Packages

Solutions to Odd-Numbered Exercises
Glossary of Terms
List of Notation
A Guide to the Literature



Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)