2 Sentences With "differentiable to"

How to use differentiable to in a sentence? Find typical usage patterns (collocations)/phrases/context for "differentiable to" and check conjugation/comparative form for "differentiable to". Mastering all the usages of "differentiable to" from sentence examples published by news publications.

type: All Declarative Interrogative Exclamative

structure: All Simple Compound Complex Compound-Complex

length: All <=10 words 10-20 words 20-30 words 30-50 words

Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at a very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of Fourier analysis into its frequency spectrum, or individual sinusoidal components, each of which contains a single frequency, amplitude and phase.
Mathematically, scalar fields on a region U is a real or complex-valued function or distribution on U. The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order. A scalar field is a tensor field of order zero, and the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form. The scalar field of \sin (2\pi(xy+\sigma)) oscillating as \sigma increases. Red represents positive values, purple represents negative values, and sky blue represents values close to zero.