Sept. 3, 2010
Richard Bernatz ’77, Luther College professor of mathematics, authored the textbook titled "Fourier Series and Numerical Methods for Partial Differential Equations," recently published by John Wiley and Sons.
Bernatz's book presents an introduction to analytical and numerical methods essential for working with partial differential equations. It combines methodologies from calculus, introductory linear algebra and ordinary differential equations to share the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of partial differential equations.
The new book serves as an ideal textbook for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It also serves as a resource for researchers and practitioners in the fields of mathematics, science and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.
Throughout the book, Bernatz incorporates his own class-tested material for an accessible, easy-to-follow presentation helping readers connect objectives with relevant applications in their own work.
Bernatz, a member of the Luther faculty since 1991, is the author of numerous journal articles in his areas of research interest, including computational fluid dynamics with applications in meteorology, climatology and mathematical models of watersheds.
In 2009 Bernatz was the recipient of an Iowa Science Foundation research grant for a project titled “Rainfall Model for Projecting the 1% Annual Discharge for Small Watersheds.”
Since joining the Luther faculty, Bernatz has been involved in several student-faculty research collaborations resulting in students presenting their results at national undergraduate research conferences.
Some of the summer projects include "Vector and Parallel Solutions of Tridiagonal Linear Systems" in 1992 by Einwei Xie, a current member of the Luther Board of Regents, "Development of the Finite Analytic Solution Method for Two-Dimensional Navier-Stokes Equations on Irregular Domains" in 1995 by Kurtis Schweitz and "Neyman-Scott Model of Rainfall in Northeast Iowa" in 2008 by Brittany Schwefel.
Bernatz holds the bachelor of arts degree from Luther College in physics and mathematics, the master of science degree from Iowa State University in meteorology and the doctoral degree from the University of Iowa in applied mathematics.