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The curve given by the polar equation r=a(1-costheta), (1) sometimes also written r=2b(1-costheta), (2) where b=a/2. The cardioid has Cartesian equation ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

Partial differential equation boundary conditions which, for an elliptic partial differential equation in a region Omega, specify that the sum of alphau and the normal ...

A plot of a function expressed in polar coordinates, with radius r as a function of angle theta. Polar plots can be drawn in the Wolfram Language using PolarPlot[r, {t, tmin, ...

Let Q(x) be a real or complex piecewise-continuous function defined for all values of the real variable x and that is periodic with minimum period pi so that Q(x+pi)=Q(x). ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.

The ordinary differential equation y^('')+(1-|y|)y^'+y=0.

Partial differential equation boundary conditions which give the normal derivative on a surface.

A particular solution to a differential equation corresponding to a specific value of the equation's free parameters. For example, the integral curves of the differential ...