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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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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.