Laplace's equation

English Alternative forms en Laplace equation Noun en potential theory The partial differential equation , commonly written or , where is the Laplace operator and is a scalar function. en 1993 V. V. Sarwate Electromagnetic Fields and Waves New Age International Publishers https://books.google.com.au/books?id=Rbqie5eQwwcC&pg=PA182&dq=%22Laplace%27s+equation%22%7C%22Laplace+equation%22&hl=en&sa=X&ved=0ahUKEwjuysKRx_vXAhXCG5QKHbm_AZ8Q6AEIRTAG#v=onepage&q=%22Laplace's%20equation%22%7C%22Laplace%20equation%22&f=false 182 In practical problems, since the charges are confined to small regions while major part of the space is charge-free, it is obvious that Laplace's Equation has far greater utility than Poisson's equation. en 1996 Peter P. Silvester; Ronald L. Ferrari Finite elements for electrical engineers 3rd https://books.google.com.au/books?id=QXWFEIesd14C&pg=PA29&dq=%22Laplace%27s+equation%22%7C%22Laplace+equation%22&hl=en&sa=X&ved=0ahUKEwjuysKRx_vXAhXCG5QKHbm_AZ8Q6AEIngEwFw#v=onepage&q=%22Laplace's%20equation%22%7C%22Laplace%20equation%22&f=false 29 Cambridge University Press Numerous problems in electrical engineering require a solution of Laplace's equation in two dimensions. This section outlines a classic problem that leads to Laplace's equation, then develops a finite element method for its solution. 2002, Gerald D. Mahan, Applied Mathematics, Kluwer Academic / Plenum, page 141, Laplace's equation appears in a variety of physics problems and several examples are provided below. The relevance of Laplace's equation to complex variables is provided by the following important theorem. Usage notes The plural is rare in this form (and when used, often, although apparently not always, an error), but appears in the alternative form Laplace equations. Translations PDE Bulgarian: bg уравнение на Лаплас n Finnish: fi Laplacen yhtälö French: fr équation de Laplace f German: de Laplace-Gleichung f Hungarian: hu Laplace-egyenlet Polish: pl równanie różniczkowe Laplace'a n Russian: ru уравне́ние Лапла́са n Further reading Harmonic function Potential theory Poisson's equation en Differential equations en eponyms