Sentence examples for differentiable functions from inspiring English sources

Differential forms are generalizations of differentiable functions in.

Differential forms are extensions of differentiable functions in R n.

The idea of differentiable functions on the sphere or torus was generalized to differentiable functions on manifolds (topological spaces of arbitrary dimension).

In contrast to real differentiable functions, which are as "flexible" as string, complex differentiable functions are "rigid" in the sense that any region of the function determines the entire function.

This leads to a remarkable geometric characterization of the class of rational complex functions: they are the differentiable functions on the sphere.

Complex differentiable functions are those for which the limit f′ z) of (f z + h) − f z))/h exists as h tends to zero.

One similarly finds that the elliptic functions (complex functions that are periodic in two directions) are the differentiable functions on the torus.

As an important example, the algebra of n-times continuously differentiable functions is studied in detail.

(Indeed, in 1872 Weierstrass produced the first example of a continuous function that cannot be differentiated at any point a function now known as a nowhere differentiable function).

For some simple cases, for example, f(x) : ℝ → ℝ is continuously differentiable function of one variable, its injectivity is equivalent to that its differential is nonzero everywhere.

Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function.