By A. David Wunsch

This supplemental textual content permits teachers and scholars so as to add a MatLab content material to a posh variables path. This booklet seeks to create a bridge among features of a posh variable and MatLab. --

summary: This supplemental textual content permits teachers and scholars so as to add a MatLab content material to a posh variables direction. This ebook seeks to create a bridge among features of a posh variable and MatLab

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**A Matlab companion to complex variables**

This supplemental textual content permits teachers and scholars so as to add a MatLab content material to a posh variables direction. This ebook seeks to create a bridge among services of a posh variable and MatLab. -- summary: This supplemental textual content permits teachers and scholars so as to add a MatLab content material to a fancy variables path.

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**Sample text**

4 The real part of z2. Exercises 1. Consider the function f(z) = z + 1/z. 5 ≤ y ≤ 2. Use 50 uniformly spaced increments in x and y. Use the default values for view. Note that you can generate multiple plots from the same program by using such commands as figure(1), figure(2), and so on, placed as code before you call plotting functions such as mesh, meshz, surf, and so on. Try plots in both color and shades of gray. a. Plot each surface using the function mesh. Use the default values for the view.

As an exercise, the reader should modify the above code so that the user is prompted to enter an integer n and a positive integer m where the fraction n/m is irreducible. The program then computes all m values of zn/m where again z must be supplied. 5 A Further Caveat with Fractional Powers: The Plot Function Suppose x is a row vector whose elements are real numbers. Let w(x) be a function defined for these values of x. A commonly used line in MATLAB 15 Complex Arithmetic code is plot(x,w), which will produce a plot in the Cartesian plane of w versus x.

If you attempt a plot of u = Re(z2) = x2 − y2, using the default angles, you will most likely be confused by the picture thus obtained (try this). Instead, after some experimentation, we find that azimuth and elevation of 45 and 60 degrees, respectively, give a better picture. To avoid the default view, enter the line of code view(az,el) right after the line of code that generates the plot. You must, of course, assign numerical values to az and el, the desired azimuth and elevation (in degrees) to use this code.