Carroll College, Helena Montana

Dr. Eric Sullivan

Dr. Sullivan is an Assistant Professor of Mathematics.  He received his B.S. in Mathematics from Iowa State Univeristy (1998), M.S. in Applied Mathematics from the University of Colorado at Colorado Springs (2007), and his Ph.D. in Applied Mathematics from the University of Colorado Denver (2013).

Dr. Sullivan's mathematical interests focus mainly on mathematical modeling with oridinary and partial differential equations.  His Ph.D. research involved the modeling of fluids in porous media using hybrid mixture theory, continuum mechanics, and numerical methods for nonlinear partial differential equations. He is also interested in innovative mathematical pedagogy and practices.  In his free time, he enjoys hiking, backpacking, biking, rock and ice climbing, kayaking, fishing, and generally being outdoors.

email: esullivan (at) carroll (dot) edu

Student Research Projects

At Carroll we require each senior math major to complete a project or thesis.  The following are current and past projects and theses directed by Dr. Sullivan.

  • Taylor Peck (2015-2016) Lanchester Battle Models
  • Elizabeth Carlson (2015-2016) Modeling Weather Balloon Descent over Mountainous Terrain 
  • Dawson Osborn (2015) Lyoponov Exponents Measuring Turbulent Mixing 
  • Tarry Vavruska (2014-2015) Using Reaction Diffusion Equations for Pattern Formation on Butterfly Wings [pdf]
  • Kyle Willis (2014-2015) Gamification of Secondary Mathematics Classes [pdf]
  • Kiersten Utsey (2013-2014) Development of Software for Generating Synthetic Fetal Electrocardiograms [pdf]
  • Joseph King (2013-2014) Burning Down the Cost: A Study to Optimize Wild fire Expenses [pdf]

Open Source Textbooks

Mathematics belongs to human kind.  The development of Calculus, in particular, is one of the crowning achievements of science and has been studied since the 1600s.  Since Calculus is so well studied and is so incredibly fundamental to the mathematical sciences it makes little sense to charge students hundreds of dollars for a textbook.  In an effort to make Calculus textbooks more accessible to our students we are using a free open source Calculus textbook.  The text began as an open source project by Professor Matt Boelkins out of Grand Valley State University (here).  Since fall of 2014, the Carroll math department has began supplementing Dr. Boelkins' text for their purposes.  The goals of Carroll's Active Calculus text are to

  1. promote active learning in a Calculus class,
  2. provide clear and concise explanations so the text can be used as a reference, and
  3. bring Calculus to our students free of charge.

We couldn't be more pleased to use this text for MA121 (differential calculus), MA122 (integral calculus), MA131 (single variable calculus), MA233 (multi-variable calculus (beta testing fall 2015 and fall 2016)), and MA141 (introduction to mathematical modeling). To view the book and other associated resources, go here.


  • Modeling First -- Techniques Just In Time (JMM January 2016)
  • Points-Free Proofs (JMM January 2016)
  • 4D Visualization -- A Zoo of Complex Functions (Carroll Math Seminar, Nov 2015)
  • Proofs Without Points (MAA Section Meeting, March 2015)
  • Teaching the Modern Teacher (XLi Extended Learning Institute, March 2015)
  • Unifying PDEs, Linear Algebra, and Complex Analysis (JMM January 2015)
  • Mini Courses and Moodle Modules for Statistics (Mountain Moodle Moot July 2014)
  • A Nonlinear PDE Model for Vapor Transport in Unsaturated Soil (JMM January 2014)
  • LaTeX and MATLAB in Multivariable Calculus (JMM January 2014)
  • The Navier Stokes Equations (Carroll Math Seminar, Nov 12, 2013)

Multivariable Calculus Labs

The following pdf documents are labs associated with our multivariable calculus course.  Anyone is welcome to use, modify, and build upon these lab activities.  If you are interested in obtaining the LaTeX source files please contact Dr. Sullivan: esullivan(at)carroll(dot)edu

  1. surface and contour plots
  2. vectors and vector operations
  3. the gradient vector
  4. approximation with tangent planes
  5. optimization
  6. Lagrange multipliers
  7. volumes through integration
  8. parameterized curves and vector fields
  9. conservative vector fields and curl. 

Dr. Eric Sullivan


Spring 2016:
  • MA122 Integral Calculus MWF 1PM
  • MA207 Elementary Statistics MWF 10AM
  • MA334 Differnetial Equations and Linear Algebra II MWF 2PM, TTh 11AM
  • MA342 Numerical Analysis, TTh 9:30AM

Fall 2015: MA121, MA141, MA250, MA401, and ED418 

Spring 2015: MA207, MA366, ED212, MA406
Fall 2014: MA141, MA233, and MA401

Spring 2014: MA122, MA406, ED212

Fall 2013: MA121, MA233