Math 385 - Introduction to Mathematical Modeling

Class: MW 2:30PM - 3:45PM in Fine Arts 303 (1/27-5/13/2025), Instructor: Bedrich Sousedik

This is a project-oriented course offering the opportunity to discover how various real-world problems can be described and analyzed with the aid of simple mathematical models and computer simulations. Possible project topics include operation of a fuse, spread of pollutants in a river, propagation of an infectious disease, traffic flow on a highway, oscillating chemical reactions, population growth in biology, etc.

Prerequisite: MATH 225 or MATH 355 with a grade of 'C' or better.

The detailed class syllabus (pdf) is here. However, look below to see the actual progress of the class.

1/27 Introduction. 2.1 Mathematical Models.

1/31 2.2 Modeling using proportionality. 2.3 Modeling using geometric similarity. Hw 1 (due 2/5).

2/3 2.3 Modeling using geometric similarity. 2.4 Automobile gasoline mileage.

2/5 2.4 Automobile gasoline mileage. 3.1 Fitting models to data graphically. Hw 2 (due 2/12).

2/10 3.3-I Applying the least-squares criterion.

2/12 3.3-II Applying the least-squares criterion. Hw 3 (due 2/19, extension 2/24).

2/17 6.1-I Probabilistic modeling with discrete systems.

2/19 6.1-II Probabilistic modeling with discrete systems. Hw 4 (due 2/26).

2/24 7.1 An overview of Optimization modeling.

2/26 7.2 Linear programming I: Geometric solutions. Hw 5 (due 3/5).

3/3 7.3 Linear programming II: Algebraic solutions. 7.4 Linear programming III: the Simplex method. Hw 6 (due 3/26).

3/5 Review for Exam 1.

3/10 Exam 1.

3/12 7.4 Linear programming III: the Simplex method. Hw 7 (due 4/2).

3/15-23 Spring break.

3/24 7.6 Numerical search methods.

3/26 11.1 Population growth. Hw 8 (due 4/7).

3/31 11.4 Graphical solutions of autonomous differential equations. Phase plane plotter.

4/2 Some applications: 1. Epidemic modeling (Going viral), 2. Cardiac cell contractility, 4. Engineering computations (FEM + DD), 5. Uncertainty quantification, 6. Digital twins. Q: AI, data analytics.

4/7 Review for Exam 2.

4/9 Project presentation: Section 6.2.

4/14 Exam 2.

4/16 Project presentation: Section 6.3.

4/21 Project presentation: Section 9.1.

4/23 Project presentation: Section 9.2.

4/28 Project presentation: Section 9.3.

4/30 Project presentation: Section 9.4.

5/5 Project presentation: Section 10.1.

5/7 Project presentation: Section 10.2.

5/12 Project presentation: Section 10.3. (The last class.)