This video production by Springer VideoMath is probably best understood as being a collection of nine short video productions on the general topic of numerical simulations. An added introduction and introductory skits performed by a robot actor bring these separate productions together to give the illusion of being a single production, but some lack of structural continuity is apparent. Although the video begins with an introduction to numerical simulation and a brief discussion of grids and quadrature, there is a sudden transition to advanced applications with no looking back to any basic tools of the trade.
Often, discussion of a complex application includes a quick overview of the simulation methods, but the emphasis here is on quick. There may be a brief review of some partial differential equations and a statement that the PDE's are solved numerically, but the viewer should not expect to gain any more than a cursory understanding of the methods or background of any particular simulation.
The viewer will, however, be introduced to the great power of numerical simulation and will, in a short time, be introduced to a dazzling array of significant successes in this field. From crystal formation to fluid flow through biofilms, from the control of robot arms and the modeling of adaptive automobile suspensions to the design of surgical procedures the viewer will be treated to a survey of a wide variety of applications.
The visual graphics make the production a pleasure to watch, but we may pause to reflect on what the educational value of this video might be. As stated before, no one will learn how to do numerical simulations by watching this video, but it is possible to learn to be interested in this important field of technology. The video could serve to motivate a young student to pursue a career in mathematical modeling and numerical simulations, but the file may be of more use for the crusty old-timer.
If there are any traditional scientists left who think that numerical simulation does not apply to their particular field then this video may help them to see that there could be some unexpected possibilities.
Paul Cohen received his Ph.D. from the University of Illinois, was appointed as a Member of the Institute for Advanced Study by Kurt Gödel, and has taught at the University of Tennessee and at Lehigh University. He currently lives in Maine and is teaching at Colby College.