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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 ...

The word differential has several related meaning in mathematics. In the most common context, it means "related to derivatives." So, for example, the portion of calculus ...

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...

A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called ...

Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial ...

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

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 ...

Differential Equations

The motivating force of topology, consisting of the study of smooth (differentiable) manifolds. Differential topology deals with nonmetrical notions of manifolds, while ...