Michael A. Karls Home Page

Michael A. Karls
Associate Professor

Department of Mathematical Sciences
Ball State University
Muncie, Indiana 47306-0490

Office: RB 470
Office Phone: (765) 285-8656
Math Department Phone: (765) 285-8640
Math Department Fax: (765) 285-1721
E-mail: mkarls@.bsu.edu

Educational Background

PhD in Mathematics (area of specialization - applied mathematics) from University of Wisconsin-Milwaukee
MS in Mathematics from University of Wisconsin-Milwaukee
BA in Physics and Mathematics from St. Mary's College

Research Interests

My main area of research is in partial differential equations. In particular, I study properties of certain non-linear forms of Poisson's equation (i.e. Du+f(u)=0 for non-linear functions f). I am also interested in new ways to illustrate classic differential equations, such as the heat and wave equations. Below is a list of my publications.

Does the Wave Equation Really Work? PRiMUS. Vol. XVI, No. 2, 162-178, June 2006. With D. Armstead. (click here for Sample Mathematica Code for this paper)

here

Integrability of Blow-up Solutions to Some Non-linear Differential Equations. Electronic Journal of Differential Equations. Vol. 2004(2004), No. 33, pp. 1-8. With A. Mohammed.
Modeling Heat Flow in a Thermos. American Journal of Physics, July 2003. With J. Scherschel. (click here for Sample Mathematica Code for this paper)

here

Uniqueness of Positive Radial Solutions of -D u=f(u) on Balls in Rⁿ. Differential equations and dynamical systems (Waterloo, ON, 1997). Dynamics of Continuous, Discrete, and Impulsive Systems. Vol. 5(1-4), 17-30, 1999.
Local Properties of Solutions of a Differential Equation Via Normed Linear Spaces. Journal of Interdisciplinary Mathematics. Vol. 1(1), 33-48, 1998. With F. Gylys-Colwell.
Zeros of Du + f(u)=0 in the Supercritical Case. Dynamical systems and differential equations, Vol. I (Springfield, MO, 1996). Discrete and Continuous Dynamical Systems, Added Volume I, 360--370, 1998.
A Uniqueness Result for Certain Semilinear Elliptic Equations. Differential and Integral Equations. Vol. 9(5), 949-966, 1996.

Here are some other projects I have worked on:

Mathematica Tutorial. Spring 2004. (click here for Mathematica 4.2 Notebook version)
First Stage Wavelet Basis Talk Part I. Fall 2003. (click here for PDF file)
First Stage Wavelet Basis Talk Part II. Fall 2003. (click here for PDF file)
Haar Wavelet Mathematica Example. Spring 2004. (click here for Mathematica 4.2 Notebook)
Shannon Wavelet Mathematica Example. Spring 2004. (click here for Mathematica 4.2 Notebook)
Daubechies Wavelet Mathematica Example. Spring 2004. (click here for Mathematica 4.2 Notebook)
Mathematics In Art: A Self-Directed Tour For The Ball State University Museum of Art. Indiana MAA Section Newsletter. Spring 1998. With R. Bergs, J. Cook, and J. Emert. (click here for MS-Word file)

Some Math and Physics-Related Links

Indiana Section of the Mathematical Association of America INMAA
MathSciNet On Campus Off Campus
American Mathematical Society AMS
Mathematical Association of America MAA
Society of Industrial and Applied Mathematicians SIAM
Math World Mathematics and Science Reference MathWorld
St. Andrews' University History of Mathematics History
A guide to HTML and CGI scripts HTML Guide
A TeXPoint--LaTeX add-on for powerpoint TeXPoint
Visible Euclidean Algorithm Euclidean Algorithm
Everything you've always wanted to know about Prime Numbers The Prime Pages
Articles on Differential Equations in the College Journal of Mathematics Differential Equations Articles
A Nice Thermal Physics Page Thermal Physics
Physics Theory on the Web Hyper Physics
Simon Singh's Web Page Cryptography and Fermat's Last Theorem

NOTICE: The information presented on this page represents the personal views, ideas, and opinions of the author. This is not an official Ball State University web page. Links contained at this web site to other organizations are presented as a service and neither constitute nor imply university endorsement or warranty.