MATH 462
CLN 10473, MWF 9:00-10:00, EH 1060

Mathematical Modeling

(Prerequisites: MATH 216, 256, 286, or 316 and Math 217, 417, or 419)


Dr. Patrick Nelson
East Hall 3071
tel: 763-3408
fax: 763-0937
office hours: Monday, 10:00-11:00; Thursday, 1:30-3:00

Homework Grades Message Board

Course description Textbook Syllabus Lecture Notes Objectives Schedule

Course Description

Introductory survey of applied mathematics with emphasis on modeling of physical, mechanical and biological problems in terms of differential equations. Formulation, analysis, and interpretation of the results will be the theme of the course. We will study analysis techniques common in dynamical systems such as linearization theory, Liapunov functions and phase plane.


There are no required texts for this class. There will be a course packet that will be available that will take notes from the following reference texts:

Other references:

  1. Mathematical Models, Richard Haberman, Siam Classics in Applied Mathematics, 1998,
  2. Nonlinear Dynamics, P.G. Drazin, Cambridge Press,
  3. Dynamical Systems, Arrowsmith and Place Chapman and Hall .

Mathematical and Modeling Concepts to be covered

  1. Concepts of Modeling
  2. Dimensions, Units, Dimensional Analysis
  3. Differential equations
  4. Formulation of models from basic principles
  5. Concepts of equilibria and stability
  6. Nonlinearity, limit cycles, bifurcations
  7. Chaos
  8. Computation with matlab
  9. Parameter estimating techniques
  10. Interpretation of results


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Learning Objectives and Instructor Expectations

Although the subject matter of Mathematical Modeling can be made rather difficult, I will attempt to present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will not be presented but I will present in detail the mathematical techniques needed for mathematical modeling. Applications will be emphasized and will come from areas of Physics, Engineering, Medicine, and the Life Sciences.


Homework assignments will count as 1/3 of grade evaluation. There will also be two quizzes and will count for 1/3 of the grade. The remaining 1/3 will come from a modeling project each student group will have to prepare and present at the end of term.

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