Recent content by JulieK

Many thanks!

I am looking for conformal transformations to map: 1. Disk of radius R to equilateral triangular region with side A. 2. Disk of radius R to rectangular region with length L and width W. 3. Disk of radius R to elliptic disk with semi-major axis a and semi-minor axis b. Thanks!

It is well known that from a two-dimensional solution of Laplace equation for a particular geometry, other solutions for other geometries can be obtained by making conformal transformations. Now, I have a function defined on a disc centered at the origin and is given by f(r) = a r where a is...

I am not sure they are not equivalent. However, I am mainly interested in the second.

My understanding is that conformal mapping is restricted to analytic functions. What sort of mapping (if any) that can be used for non-analytic functions?

Thanks Astronuc for your useful remark! I solved the problem by testing Wolfram numerically using numerical integration. I noticed that Wolfram expression produces large errors in some cases. Replacing Wolfram expression with numerical integration I obtained almost perfect results.

I have the following problem \begin{equation} \frac{\mathrm{arcsinh}\left(y\right)}{y}\frac{dy}{dx}=B\end{equation}where B is constant. To solve the problem I separated the variables and obtained \begin{equation} \int\frac{\mathrm{arcsinh}\left(y\right)}{y}dy=B \int dx\end{equation}I used...

I have a multivariable function, z = f(x, y, w), represented by a surface plot in 3D (z versus xy) for each value of w. As w varies, the function z varies (goes up and down and changes shape) over a given rectangular xy region. As z varies with w, contour lines with given constant values of z...

Thank you all!

Is there a conformal mapping that transforms regular polygons (e.g. triangle and square) to circle?

Can you suggest a general analytical solution to the following equation \ln(x^{3/2})-bx-c=0 where x is real positive variable and b and c are real positive constants.

I am looking for a good and easy access reference on multi-variable calculus of variation with many examples and demonstrations. Although I have many books and references on the calculus of variation, most are focused on single-variable. Any advice will be appreciated.

Is there a formal relation that links \int yxdx OR \int_{a}^{b}yxdx with \int xydy OR \int_{a}^{b}xydy where y=f(x) over the interval x\in\left[a,b\right].

What is this integral \int\left(\frac{\mathrm{arcsinh}(ax)}{ax}\right)^{b}dx where a and b are constants.

I know the value of the following definite integral \int_{a}^{b}ydx I also have a realtion x=f(y) i.e. x is an explicit function of y but I do not have y as an explicit function of x. The relation between x and y is generally non linear. Now I want to get the following definite...