The Geometrical Significance of the Laplacian

Abstract

The Laplacian operator can be defined, not only as a differential operator, but also through its averaging properties. Such a definition lends geometric significance to the operator: a large Laplacian at a point reflects a “nonconformist” (i.e., different from average) character for the function there. This point of view is used to motivate the wave equation for a drumhead.

Publisher

American Association of Physics Teachers

Publication Date

12-1-2015

Publication Title

American Journal of Physics

Department

Physics and Astronomy

Document Type

Article

DOI

https://dx.doi.org/10.1119/1.4935133

Keywords

Kinematics, Laplace equations, Poisson's equation, Wave equations, Fluid equations

Language

English

Format

text

Link to Full Text

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