A Matlab companion to complex variables by A. David Wunsch

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By A. David Wunsch

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

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The reader may wish to review these terms in a standard text. A region is composed of an infinite number of points in the x−y plane, and we have no hopes of storing that number of points in our computer in preparation for plotting u and v as functions of x and y. What we do is create a mesh consisting of a rectangular grid of lines in the region of interest. The spacing of the lines is usually but not always uniform. 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).

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. Now the vector b has only real elements, which are 1 and 5 and 10. The imaginary part of each element is zero. So, following the logic used by MATLAB in making the plot for a, we would expect that these points would occur on the line y = 0 at x = 1 and 5 and 10. We would expect MATLAB to connect these points with a horizontal line.

If we define f ( z) = z ≠ 0 and f(0) = 1, we z have a new function that agrees with the old except at z = 0. Moreover, the z2 z 4 new function is the sum of the convergent power series 1 − + + ... and 3! 5! is therefore analytic wherever this series converges—in this case, the whole complex plane including the origin. We see that by properly defining a function at an isolated singular point, we can remove its singularity at that point. The original function is said to have a removable singularity at this isolated singular point.

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