Michael A. Karls
Professor
Department of Mathematical
Sciences
Ball State University
Muncie, Indiana 47306-0490
Office: RB 465
Office Phone: (765) 285-8640
Math Department Phone: (765) 285-8640
Math Department Fax: (765) 285-1721
E-mail: mkarls@bsu.edu
Educational Background
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.
Laplacian(u)+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 some of my publications.
- An Applied Project-Driven Approach to Undergraduate Research Experiences.
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.
Vol. 27, No. 4-5, 461-475, July 2017.
(click here for
an online version of this paper)
- Solutions of p-Laplace Equations with Infinite Boundary Values:
The case of Non-Autonomous and Non-Monotone Nonlinearities.
Proceedings of the Edinburgh Mathematical Society.
Vol. 59, No. 4, 959-987, November 2016. With Ahmed Mohammed.
- The Role of Graduate Students in Research Experience for Undergraduates Programs.
Involve, a Journal of Mathematics.
Vol. 7, No. 3, 369-372, April 2014. With David McCune, Lara Pudwell, and Azadeh Rafizadeh
(click here for
an online version of this paper)
- Innovation, Parallel Shifts of Supply, and Welfare.
Agricultural Economics Review.
Vol. 14, No. 1, 37-44, 2013.
With John B. Horowitz, Juan Sesmero and T. Norman Van Cott.
(click here for
an online version of this paper)
- Verifying the Hanging Chain Model.
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.
Vol. 23, No. 8, 733-747, July 2013.
(click here for
an online version of this paper)
(click here for a PDF slide show on this paper)
- The Mathematics of Star Trek - An Honors Colloquium.
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.
Vol. 21, No. 1, 26-46, January 2011.
- Implementing an Introductory Mathematical Software Course.
The Electronic Journal of Mathematics and Technology.
Vol. 4, No. 3, 232-250, October 2010.
(click here for a PDF slide show on this paper)
(click here for a PowerPoint slide show on this paper)
- Codes, Ciphers, and Cryptography - An Honors Colloquium.
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.
Vol. 20, No. 1, 21-38, January 2010.
- Modeling a Diving Board.
Mathematics Magazine. Vol. 82, No. 5, 343-353, December 2009. With Brenda M. Skoczelas.
(click here for
article supplements)
(click here for a PDF slide show on this paper)
- Does the Wave Equation Really Work?
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.
Vol. XVI, No. 2, 162-178, June 2006. With Donald C. Armstead.
(click here for Sample Mathematica Code for this paper)
(click here for a Power Point slide show on this paper)
- 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 Ahmed Mohammed.
- Modeling Heat Flow in a Thermos. American Journal of Physics, Vol. 71, No. 7, 678-683, July 2003. With James E. Scherschel.
(click here for Sample Mathematica Code for
this paper)
(click here for a Power Point slide show on this paper)
- Uniqueness of Positive Radial Solutions of
-Laplacian(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 Frederick D. Gylys- Colwell.
- Zeros of Laplacian(u) + 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. Fall 2008. (click here for Mathematica 6.0 Notebook version)
- Elliptic Curves and Elliptic Curve Cryptography (Honors Thesis Advisor). 2003-04.
(click here for PDF file)
- 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 PDF file)
Some Math and Physics-Related Links
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.