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There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

Denote the nth derivative D^n and the n-fold integral D^(-n). Then D^(-1)f(t)=int_0^tf(xi)dxi. (1) Now, if the equation D^(-n)f(t)=1/((n-1)!)int_0^t(t-xi)^(n-1)f(xi)dxi (2) ...

An identity in calculus of variations discovered in 1868 by Beltrami. The Euler-Lagrange differential equation is (partialf)/(partialy)-d/(dx)((partialf)/(partialy_x))=0. (1) ...

The operator representing the computation of a derivative, D^~=d/(dx), (1) sometimes also called the Newton-Leibniz operator. The second derivative is then denoted D^~^2, the ...

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0) in the direction u. It is a vector form of the ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

A double integral over three coordinates giving the area within some region R, A=intint_(R)dxdy. If a plane curve is given by y=f(x), then the area between the curve and the ...

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

A sequence of polynomials p_n satisfying the identities p_n(x+y)=sum_(k>=0)(n; k)p_k(x)p_(n-k)(y).