A MatLab® Companion to Complex Variables

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.

Complex ArithmeticThe Rectangular FormExercisesThe Polar Form of Complex NumbersExercisesFractional Powers of Complex NumbersExercisesComplex Symbolic AlgebraExercisesLoci and Regions in the Complex Plane and Displaying Complex FunctionsMeshgrid and Three-Dimensional PlottingExercisesTwo-Dimensional Plots: The Contour PlotExercisesDisplaying Regions in the Complex PlaneThree-Dimensional and Contour Plots for Functions with SingularitiesContour Plots Affected by Branch CutsExercisesSequences, Series, Limits, and IntegralsSequencesExercisesInfinite Series and Their ConvergenceExercisesIntegration in the Complex Plane: Part 1, Finite Sums as ApproximationsExercisesIntegrations in the Complex Plane: Part 2, int and quadgkExercisesHarmonic Functions, Conformal Mapping, and Some ApplicationsIntroductionExercisesThe Bilinear TransformationLaplace’s Equation, Harmonic Functions: Voltage, Temperature, and Fluid FlowExercisesComplex Potentials, Cauchy–Riemann Equations, the Stream Function, and StreamlinesExercisesMapping, Dirichlet, and Neumann Problems and Line Sources ExercisesPolynomials, Roots, the Principle of the Argument, and Nyquist StabilityIntroductionThe Fundamental Theorem of AlgebraExercisesThe Principle of the ArgumentExercisesNyquist Plots, the Location of Roots, and the Pole-Zero MapExercisesTransforms: Laplace, Fourier, Z, and HilbertIntroductionThe Laplace TransformExercisesThe Fourier TransformExercisesThe Z TransformExercisesThe Hilbert TransformExercisesCoda: Fractals and the Mandelbrot SetJulia SetsAppendix to CodaExercisesIndex

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.