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A point p on a regular surface M in R^3 is said to be planar if the Gaussian curvature K(p)=0 and S(p)=0 (where S is the shape operator), or equivalently, both of the ...

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.

A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, which has f^'(x) = ...

A fixed point for which the stability matrix has equal negative eigenvalues.

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=-alpha+/-ibeta (with alpha,beta>0).

A fixed point for which the stability matrix has one zero eigenvector with negative eigenvalue lambda<0.

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

The planes passing through the vertices of a tetrahedron ABCD and tangent to the circumsphere at these points form another tetrahedron called the tangential tetrahedron. The ...

Integrals of the form intf(costheta,sintheta)dtheta (1) can be solved by making the substitution z=e^(itheta) so that dz=ie^(itheta)dtheta and expressing costheta = ...