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A MatLab® Companion to Complex Variables





ISBN 9781498755672
Published April 19, 2016 by CRC Press
344 Pages - 105 B/W Illustrations

 
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Book Description

This book is intended for someone learning functions of a complex variable and who enjoys using MATLAB. It will enhance the exprience of learning complex variable theory and will strengthen the knowledge of someone already trained in ths branch of advanced calculus.

ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB®. Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses.

A MATLAB® Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables, the book allows professors to quickly find and assign MATLAB programming problems that will strengthen students’ knowledge of the language and concepts of complex variable theory.

The book shows students how MATLAB can be a powerful learning aid in such staples of complex variable theory as conformal mapping, infinite series, contour integration, and Laplace and Fourier transforms. In addition to MATLAB programming problems, the text includes many examples in each chapter along with MATLAB code.

Fractals, the most recent interesting topic involving complex variables, demands to be treated with a language such as MATLAB. This book concludes with a Coda, which is devoted entirely to this visually intriguing subject.

MATLAB is not without constraints, limitations, irritations, and quirks, and there are subtleties involved in performing the calculus of complex variable theory with this language. Without knowledge of these subtleties, engineers or scientists attempting to use MATLAB for solutions of practical problems in complex variable theory suffer the risk of making major mistakes. This book serves as an early warning system about these pitfalls.

Table of Contents

Complex Arithmetic
The Rectangular Form
Exercises
The Polar Form of Complex Numbers
Exercises
Fractional Powers of Complex Numbers
Exercises
Complex Symbolic Algebra
Exercises

Loci and Regions in the Complex Plane and Displaying Complex Functions

Meshgrid and Three-Dimensional Plotting
Exercises
Two-Dimensional Plots: The Contour Plot
Exercises
Displaying Regions in the Complex Plane
Three-Dimensional and Contour Plots for Functions with Singularities
Contour Plots Affected by Branch Cuts
Exercises

Sequences, Series, Limits, and Integrals

Sequences
Exercises
Infinite Series and Their Convergence
Exercises
Integration in the Complex Plane: Part 1, Finite Sums as Approximations
Exercises
Integrations in the Complex Plane: Part 2, int and quadgk
Exercises

Harmonic Functions, Conformal Mapping, and Some Applications

Introduction
Exercises
The Bilinear Transformation
Laplace’s Equation, Harmonic Functions: Voltage, Temperature, and Fluid Flow
Exercises
Complex Potentials, Cauchy–Riemann Equations, the Stream Function, and Streamlines
Exercises
Mapping, Dirichlet, and Neumann Problems and Line Sources
Exercises

Polynomials, Roots, the Principle of the Argument, and Nyquist Stability

Introduction
The Fundamental Theorem of Algebra
Exercises
The Principle of the Argument
Exercises
Nyquist Plots, the Location of Roots, and the Pole-Zero Map
Exercises

Transforms: Laplace, Fourier, Z, and Hilbert

Introduction
The Laplace Transform
Exercises
The Fourier Transform
Exercises
The Z Transform
Exercises
The Hilbert Transform
Exercises

Coda: Fractals and the Mandelbrot Set

Julia Sets
Appendix to Coda
Exercises

Index

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Author(s)

Biography

A. David Wunsch is Professor Emeritus of Electrical and Computer Engineering at the University of Massachusetts Lowell, USA. He earned his PhD from Harvard University and is the author of the textbook Complex Variables with Applications, published by AddisonWesley/Pearson. The book is currently in its third edition and has been continuously in print since 1983. It is one of the most popular textbooks on the subject.

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