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The relative rate of change of a function f(x) is the ratio if its derivative to itself, namely R(f(x))=(f^'(x))/(f(x)).

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...

A fractional derivative of order 1/2. The semiderivative of t^lambda is given by D^(1/2)t^lambda=(t^(lambda-1/2)Gamma(lambda+1))/(Gamma(lambda+1/2)), so the semiderivative of ...

Let f_1(z), ..., f_m(z) for m>=1 be a set of E-functions that (1) form a solution of the system of differential equations y_k^'=q_(k0)+sum_(j=1)^mq_(kj)y_j for q_(kj) in C(z) ...

A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A tensor defined in terms of the tensors which satisfy the double contraction relation.

A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

The sum rule for differentiation states d/(dx)[f(x)+g(x)]=f^'(x)+g^'(x), (1) where d/dx denotes a derivative and f^'(x) and g^'(x) are the derivatives of f(x) and g(x), ...