Michael A. Karls

Courses for Fall 2025

• MATH 166 - Calculus 2

• MATH 374 - Differential Equations

Educational Background 

• PhD in Mathematics from University of Wisconsin-Milwaukee (area of specialization - applied mathematics)

• MS in Mathematics from University of Wisconsin-Milwaukee 

• BA in Physics and Mathematics from St. Mary's College (now St. Mary's University of Minnesota) 

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. ∆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.

• Modeling One-Dimensional Groundwater Flow Revisited.  SIMIODE: Systematic Initiative for Modeling Investigations and Opportunities with Differential Equations. 9-003-S-GroundWaterflowRevisited (and 9-003-T-GroundWaterflowRevisited). (2025).

• Using a Sand Tank Groundwater Model to Investigate a Groundwater Flow Model, CODEE Journal: Vol. 17, Article 13, 2024, 1-23.  With Christopher Evrard, Callie Johnson, and Nicole Regnier.

• Beyond Simple Profit Maximization in Uncertain Markets: How Innovation and Entry Change Supply Curves and Producer Surplus. The Journal of Private Enterprise 38(2), 2023, 55-77. With John B. Horowitz, Juan Sesmero, and T. Norman Van Cott.

• Cooking a Turkey. SIMIODE: Systematic Initiative for Modeling Investigations and Opportunities with Differential Equations. 9-014-S-TurkeyCook-ModelingScenario (and 9-014-T-TurkeyCook-ModelingScenario). (2022).

• Modeling One-Dimensional Groundwater Flow. SIMIODE: Systematic Initiative for Modeling Investigations and Opportunities with Differential Equations. 9-002-S-GroundWaterFlow (and 9-002-T-GroundWaterFlow). With Jeremy Christman and Kenneth H. Luther (2020).

• Modeling Bubbles of Beer. SIMIODE: Systematic Initiative for Modeling Investigations and Opportunities with Differential Equations. 6-070-S-BeerBubbles (and 6-070-T-BeerBubbles) (2018). 

• 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.

• 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. 

• 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.

• Verifying the Hanging Chain Model. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies. Vol. 23, No. 8, 733-747, July 2013.

• 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.

• 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. 

• 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) 

• 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.

• Uniqueness of Positive Radial Solutions of -∆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 ∆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: 

• How Continuous Innovation Affects Supply, Producer Surplus, and Consumer Surplus.  Spring 2015.  With John B. Horowitz, Juan Sesmero, and T. Norman Van Cott (click here for Wolfram Demonstrations Project file)

• Mathematica Tutorial. Spring 2009. (click here for Mathematica 6.0 Notebook version)

• Digital Video Authenticator. Spring 2007. With Thomas E. Duerr, Nicholas D. Beser, James H. Higbie, Donna C. Paulhamus, Cash J. Costello, and George R. Barrett.  (click here for PDF file) 

• 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

• Indiana Section of the Mathematical Association of America INMAA 

• Indiana Section of the MAA Student Workshop (click here for PowerPoint slides) 

• Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations SIMIODE 

• MathSciNet On Campus Off Campus 

• American Mathematical Society AMS 

• Mathematical Association of America MAA 

• Society for Industrial and Applied Mathematics SIAM 

• Math World Mathematics and Science Reference MathWorld 

• University of St. Andrews' MacTutor History of Mathematics

• A guide to HTML and CGI scripts HTML Guide 

• IguanaTex -- a free LaTeX add-in for PowerPoint (replaces TexPoint for older operating systems)

• Online Euclidean Algorithm Calculator Euclidean Algorithm 

• Everything you've always wanted to know about Prime Numbers The Prime Pages 

• Reviews of Articles on Differential Equations ODE Reviews

• 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.