V63.0251: Introduction to Math Modeling
| Term: | Spring 2011 |
| Lectures: | MW 12:30pm-1:45pm in WWH 201 |
| Recitations: | Fr 12:30pm-1:45pm in WWH 201 |
| Instructor: | Prof. E. Tabak |
| Office: | WWH 503 |
| Office hours: | To be arranged in class. |
| Phone: | 212-998-3088 |
| Email: | tabak@cims.nyu.edu |
Prerequisites
V63.0121 Calculus I, V63.0122 Calculus II and V63.0123 Calculus III with a grade of C or better or permission of the instructor
Course description
Formulation and analysis of mathematical models. Mathematical tool include dimensional analysis, optimization, simulation, probability, and elementary differential equations. Applications to biology, sports, economics, and other areas of science. The necessary mathematical and scientific background will be developed as needed. Students will participate in formulating models as well as in analyzing them.
Course Details
Textbook and Materials
No book required.
Homework
Assigned weeklyExams
Final exam on Wed. May 11, 12:00-1:50pm
Grading policy
The results of homework, quizzes, midterm, and final will be combined
Calendar
| Week | Topic |
|---|---|
| 1 | Mathematical Models in the Physical Sciences: Traffic flow |
| 2 | Rivers and lakes. Conservation laws, shock waves. |
| 3 | Stochastic models. Markov chains. Population dynamics. |
| 4 | Equilibrium, oscillations, growth and decay. |
| 5 | Data fitting. Least squares. Regression and classification. |
| 6 | Probabilistic approach. Density estimation. |
| 7 | Maximal likelihood, information theory. |
| 8 | Introduction to Mathematical Models in Biology |
| 9 | Population dynamics, Predator-Prey Models |
| 10 | Optimization. Linear programming. Lagrange multipliers. |
| 11 | Duality. Game theory. |
| 12 | Project presentation. |
| 13 | Project presentation. |