NDLI: Education (SIREAD Vol. 54 Issue. 2)

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Education (SIREAD Vol. 54 Issue. 2)

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rossi, Louis F.
Copyright Year	2012
Abstract	The Education section in this issue of SIAM Review features two articles with two unique flavors. The first brings together distinct topics first introduced in the undergraduate curriculum and is suitable for an undergraduate audience. The second is a brief renormalization group tutorial for a graduate curriculum. In Modified Gershgorin Disks for Companion Matrices, author Aaron Melman connects zeros of polynomials with the properties of their corresponding companion matrix. He begins with the basic notion that the zeros of a polynomial are contained within the union of Gershgorin disks of the corresponding companion matrix. While this is an elegant connection, the union of disks can be a fairly large set. The author points out that a careful examination of the structure of the companion matrix and some judicious manipulation can restrict these sets much further. The resulting discussion makes a nice module for an undergraduate course in linear algebra or analysis. This article also includes MATLAB code for rendering the restricted sets where the roots reside. The second article, The Renormalization Group: A Perturbation Method for the Graduate Curriculum, by Eleftherios Kirkinis, provides a gentle introduction to renormalization group (RG) methods for singular perturbation problems. The authors make the case that RG methods provide a more consistent approach to perturbation problems than traditional techniques such as matched asymptotic expansions, WKB, and multiple scales. Readers unfamiliar with RG methods will find a basic introduction to the method along with three detailed examples: A linear oscillator, a nonlinear Duffing oscillator, and wave propagation in a nonlinear medium. The authors compare the RG solutions to those won through more traditional approaches in popular texts, so that instructors can use this article to augment a standard course on perturbation methods or as supplementary material for eager graduate students.
Starting Page	353
Ending Page	353
Page Count	1
File Format	PDF
ISSN	00361445
DOI	10.1137/SIREAD000054000002000353000001
e-ISSN	10957200
Journal	SIAM Review (SIREAD)
Issue Number	2
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-05-08
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computational Mathematics

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