A Matlab companion to complex variables by A. David Wunsch

By A. David Wunsch

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

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The (x,y) coordinates at the intersections of these lines provide the values for z = x + iy at which we will evaluate the real and imaginary parts of f(z). 27 28 A MATLAB® Companion to Complex Variables To create this mesh, we use the MATLAB® function meshgrid. Meshgrid accepts two arguments x and y. These are row vectors whose elements are the x and y coordinates of the points of intersection of the grid that is of interest. For example, suppose you wished to know the values assumed by a function at the points in the x−y plane where the vertical lines x = 0, x = 1, x = 2 intersect the horizontal lines y = 3, y = 5, y = 6, y = 7.

Does your estimate of π improve if you average these results? Change your code so as to use 10,000 points. Are your results improved? 4 Three-Dimensional and Contour Plots for Functions with Singularities Most, but not all, of the interesting functions in complex variable theory are ones that are analytic, except possibly at some singular points. Some functions possess isolated singular points; at an isolated singular point the function is analytic throughout a deleted neighborhood (a punctured disc) centered at that singular point.

3 Plots for x1/3. 4 Values of 10eiθ generated by letting θ go through 100 values between 0 and 2π. 2 18 A MATLAB® Companion to Complex Variables And while we are on the subject of plot, here is a further peril involving plot when you are using vectors with complex elements together with vectors having real elements. 5. The plot of the vector a shows its imaginary elements plotted against their corresponding real parts. They all lie on the line y = x, which makes a 45-degree angle with the real axis.

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