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An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

The space of currents arising from rectifiable sets by integrating a differential form is called the space of two-dimensional rectifiable currents. For C a closed bounded ...

A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Kaps-Rentrop methods.

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

A method of numerically integrating ordinary differential equations by using a trial step at the midpoint of an interval to cancel out lower-order error terms. The ...

A metric g_(ij) which is zero for i!=j.

The operator D=-i(d+d^*), where d^* is the adjoint.

sum_(i=1)^n((partialu)/(partialx_i))^2=1.