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Hi Scott, I took complex analysis in college, but am brushing up on it for my job and have a question. I am looking at a section on conformal mapping and have looked at examples including z^2, e^z, sin(z), and log(z). I understand the theory behind it, but I have a problem that's thrown me for a loop. I don't remember the particulars, but it was essentially solving Laplace's Equation on a 45 degree sector in a cartesian plane. My initial thought was to use a transformation with the sine function. I looked at the solution manual and it's suggesting using z^4 as a transform. I don't see any examples in my book with using this transform and I couldn't find anything online. Can you please give me some of the motivation behind using this transform?

Thanks!

A transformation is done by applying some function to a variable.

It is often represented by y = f(x).

For any constants in the function that are added on, it shifts the variable over.

For any constants in the function that are in front of x, it expands or compresses the curve.

For constants that are on powers of x, it shifts the curve outward.

Transformations are used in nature for falling bodies, reflected light, refracted light, compression, expansion, projectiles, gravitational affect, and many other things studied in mathematics, chemistry, physics, medical, and other fields.

Transformations also occur where a multi-variable function is transformed into a lesser degree function.

LaPlace transforms are generally used in solving differential equations.

A good example is found here: http://www.sosmath.com/diffeq/laplace/application/laplace1/answer.html

An additional place to find them is http://www.math.colostate.edu/~pauld/M545/L%20Transform

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