Laplace in a sentence

Because the Laplace transform is a linear operator, * The Laplace transform of a sum is the sum of Laplace transforms of each term. :: * The Laplace transform of a multiple of a function is that multiple times the Laplace transformation of that function.

The bilateral Laplace transform is defined as follows, : Inverse Laplace transform main Two integrable functions have the same Laplace transform only if they differ on a set of Lebesgue measure zero.

The Laplace transform can be alternatively defined as the bilateral Laplace transform or two-sided Laplace transform by extending the limits of integration to be the entire real axis.

As a result, the velocity potential φ has to satisfy Laplace's equation : where is the Laplace operator (sometimes also written Δ ).

If g is the antiderivative of f : : then the Laplace–Stieltjes transform of g and the Laplace transform of f coincide.

Table of selected Laplace transforms main The following table provides Laplace transforms for many common functions of a single variable. citation citation For definitions and explanations, see the Explanatory Notes at the end of the table.

David is an engineer for Valero’s refinery in Norco, very near to LaPlace.

Jo and Joy Banner, co-founders of The Descendants Project, announce the non-profit’s acquisition of the Woodland Plantation in LaPlace, La.

Cathy LaPlace addressed the board in the public-comment section of the meeting.

The initial focus of the channel deepening will be near Southwest Pass and at 12 river “crossings” between LaPlace and Baton Rouge.

Also techniques of complex variables can be used directly to study Laplace transforms.

Although Gauss was the first to suggest the normal distribution law, Laplace made significant contributions.

An example of pathological behavior is the sequence (depending upon n) of Cauchy problems for the Laplace equation : with boundary conditions : : where n is an integer.

Another "Poisson's integral" is the solution for the Green function for Laplace's equation with Dirichlet condition over a circular disk: : where : : :φ is a boundary condition holding on the disk's boundary.

A potential that doesn't satisfy Laplace's equation together with the boundary condition is an invalid electrostatic potential.

Applying Laplace transformation results in the transformed PID controller equation : : with the PID controller transfer function : There exists a nice example of the closed-loop system discussed above.

As a holomorphic function, the Laplace transform has a power series representation.

As a result, LTI systems are stable provided the poles of the Laplace transform of the impulse response function have negative real part.

A well-known one took place between Steven Weinberg and Philip Anderson Impossibility of being "of everything" Although the name "theory of everything" suggests the determinism of Laplace's quotation, this gives a very misleading impression.

Because of this property, the Laplace variable s is also known as operator variable in the L domain: either derivative operator or (for s −1 ) integration operator.