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Published in:
1998 | OriginalPaper | Chapter
The Heat and Wave Equations in Higher Dimensions
Author : Jeffery Cooper
Published in: Introduction to Partial Differential Equations with MATLAB
Publisher: Birkhäuser Boston
Included in: Professional Book Archive
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We shall use x to denote points in R2 or R3 with components (x, y) or (x, y, z), and the Euclidean length of a vector is denoted $$\left| x \right| = \sqrt {x^2 + y^2 } $$ or $$\left| x \right| = \sqrt {x^2 + y^2 + z^2 } $$. The Laplace operator (Laplacian) in R2 or R3 is $$\Delta u = u_{xx} + u_{yy} {\text{ or }}\Delta u = u_{xx} + u_{yy} + u_{zz} .$$