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Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...

The partial differential equation (1+u_y^2)u_(xx)-2u_xu_yu_(xy)+(1+u_x^2)u_(yy)=0 (correcting a typo in Zwillinger 1997, p. 134).

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

For x>0, J_0(x) = 2/piint_0^inftysin(xcosht)dt (1) Y_0(x) = -2/piint_0^inftycos(xcosht)dt, (2) where J_0(x) is a zeroth order Bessel function of the first kind and Y_0(x) is ...

An infinitesimal which is not the differential of an actual function and which cannot be expressed as dz=((partialz)/(partialx))_ydx+((partialz)/(partialy))_xdy, the way an ...

h_t+(|h|^nh_(xxx))_x=0, where h(x,t) is the height of a film at position x and time t and n is a parameter characteristic of the surface forces.

The partial differential equation u_t+uu_x=nuu_(xx) (Benton and Platzman 1972; Zwillinger 1995, p. 417; Zwillinger 1997, p. 130). The so-called nonplanar Burgers equation is ...

The partial differential equation u_t=del ·[M(u)del ((partialf)/(partialu)-Kdel ^2u)].

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

The partial differential equation u_t=(1+ia)u_(xx)+(1+ic)u-(1+id)|u|^2u.