The Education section in this issue features two very different articles that highlight the interplay between mathematical reasoning and computational exploration. The intriguing patterns on the cover of this issue are a teaser for our first article, which explores eigenvalue problems arising from partial differential equations. In this article, the complete model is known but explicit solutions are not available. In this case, computation allows us to rapidly calculate approximate numerical solutions. The second article, highlighting statistical methods for studying trends in temperature data, works in the other direction: Model parameters cannot be independently measured, but there is plenty of data to describe the solution. In both cases, the authors provide code and other resources necessary to reproduce their examples. In “Chladni Figures and the Tacoma Bridge: Motivating PDE Eigenvalue Problems via Vibrating Plates,” authors Martin Gander and Felix Kwok offer a new look at classic resonance problems arising from vibrating plates, exemplified by the vibration of bridge platforms. Most introductory PDE texts explore vibrating membranes in great depth as a classic problem illustrating periodic motion. Gander and Kwok explore vibrating plates as another process with periodic solutions. Separation of variables yields an eigenvalue problem involving the biharmonic operator. The resulting problem is tougher to tackle than the classic wave equation, but it gives students a much bigger field in which to play. The authors formulate and contrast two distinct techniques for computing the eigenvalue/eigenfunction pairs for the biharmonic operator: Ritz's “spectral” approximation and direct finite differences. To make the module complete, the authors provide the Maple and MATLAB code used to generate the eigenfunctions, so this material would work well in an introductory PDE course or a numerical PDE course. In their final example, the authors return to their original motivation, the vibrational modes of a bridge. Requiring fixed ends for the supports adds another twist to the problem. In contrast to the oscillation and collapse of the Tacoma Narrows Bridge, which lasted about an hour, local and global warming trends span years, decades, and centuries. In our second article, author Robert Vanderbei takes a statistical look at temperature data near his home in Princeton, NJ. In this case, he uses a least-absolute-deviation regression on the data to identify linear trends in seasonal data, the phase of the solar cycle, and humidity trends. The author provides the AMPL code used to produce his results, and to ease the challenge of assembling the data, the author provides scripts for pulling the data together from online sources, making it a nice addition to an undergraduate or introductory graduate statistics course. This article is an excellent example of the statistical exploration of data to resolve problems that are easy to pose but difficult to answer. Nothing captures the attention of students more than a major calamity, and by coincidence both articles this month focus on disaster or at least the potential for disaster. I have no doubt that the footage of the Tacoma Narrows Bridge shaking itself apart continues to provide the world with many excellent mathematicians, physicists, and engineers who otherwise might have turned to other fields. Using mathematics supported by judicious computation to understand disasters is excellent stuff for the classroom, especially when the underlying causes and mechanisms fail to reveal themselves to a cursory inspection.
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