### Some articles on *laplace, equation, laplace equation, equations*:

... could be modeled using potentials which satisfy

**Laplace**'s

**equation**... considerable overlap between potential theory and the theory of the

**Laplace equation**... on the properties of the functions as opposed to the properties of the

**equation**...

... r, θ, and φ for the spherical polar coordinates of the 3-vector r, we can write the

**Laplace equation**in the following form where L2 is the square of the angular momentum operator, It is known that ...

... Because of the linearity of the

**Laplace equation**— valid in the fluid interior and depending on the boundary condition at the bed z=-h and free surface z ... of the surface potential φ through the

**Laplace equation**, but w depends non-linear on the surface elevation η with W operating linear on φ, but being non-linear in η ... variables and gives provided in the fluid interior Φ satisfies the

**Laplace equation**, ΔΦ=0, as well as the bottom boundary condition at z=-h and Φ=φ at the free surface ...

... In the mathematical study of partial differential

**equations**, the Bateman transform is a method for solving the

**Laplace equation**in four dimensions ... variables, then is a solution of the

**Laplace equation**, which follows by differentiation under the integral ... Furthermore, Bateman asserted that the most general solution of the

**Laplace equation**arises in this way ...

### Famous quotes containing the words equation and/or laplace:

“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the *equation* was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”

—Anna Quindlen (b. 1952)

“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”

—Pierre Simon De *Laplace* (1749–1827)