Revised: September 2014
Mathematical modeling is the process of describing physical phenomena through the use of mathematical concepts and language, and then analyzing the mathematical system to learn more about the physical system. Topics for this course are chosen based on student and instructor interest, and may include: differential equation models, analysis of stability and sensitivity, difference equations, Markov processes, or optimization. Prerequisites: MATH 320, MATH 362, and MATH 340.
By the end of the course students will be able to read the literature in mathematical modeling, understanding why the investigators used specific methods of analysis and how they give information about the physical process under consideration. Students will be able to:
Beltrami, Edward. Mathematics for Dynamic Modeling. (2nd edition) Academic Press, 1997. Additional supplemental material may be provided.
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
• Chapter 1: Simple Dynamic Models
Design of models with Newton’s Laws, conservation of mass, law of mass action, equilibrium analysis I, stability.
• Chapter 2: Ordinary Differential Equations
Linear systems, eigenvalue analysis, phase portraits.
• Chapter 3: Stability of Dynamic Models
Systems of differential equations, linearization, equilibrium analysis II, competition models, SIR models, Lyapunov functions, feedback control.
• Chapter 6: Cycles and Bifurcation
Limit cycles, Poincare-Bendixson Theorem.
• Chapter 7: Bifucation and Catastrophe
Parameter dependence, bifurcations.
• Additional Topics as Time Allows.