From Hot Spots to High School Geometry and Calculus

Year: 2004 Authors: Tiziana Giorgi; Robert Smits

Core claim

Geometry and calculus can be used to interpret numerical and analytical behavior of the Hot Spots Conjecture and related Robin and Neumann eigenvalue problems.

Topics

Hot Spots Conjecture, eigenvalue problems, level sets, numerical simulation, long-term heat flow

Domains

Laplace operator, Neumann eigenvalue problem, Robin eigenvalue problem, Euclidean geometry, advanced calculus, visualization

Methods

numerical simulation, geometric conjecture, analytic derivation, mean value theorem, eigenfunction analysis

Media

Matlab PDE-Toolbox, level-set plots, heat equation

Source status

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