Introduction to Continuous Mathematical Modeling

Course Description

Textbook

However, this is where you will be able to download my lecture notes.

• Lecture Set 1 (PDF)
• Lecture Set 2 (PDF) (posted 5.10.2002)
• Lecture Set 3 (PDF) (posted 12.10.2002)
• Lecture Set 4 (PDF) (posted 25.10.2002, corrected figures 7.11.2002): We will also use lecture notes prepared by Professors K. K. Tung (click here) and Mark Kot (click here) for previous sections of this course, and who have given permission for us to use them.
• Lecture Set 5 (PDF) (posted 7.11.2002) We will return to the predator-prey discussion and linearization in Prof. Tung's notes above after competition models.
• Lecture Set 6 (PDF) (posted 15.11.2002) This is the wrap-up of the previous set on stability of fixed points by linearization.
• Lecture Set 7 (PDF) (posted 26.11.2002) Predator-Prey model. (see also Prof. Tung's notes above)

Syllabus

Modeling:

Philosophy, dimensional analysis, examples

First-order ODEs:

Population dynamics, exponential and logistic growth, sketching solutions, phase-line, stability and bifurcations.

Linear interacting systems:

Phase-plane analysis, equilibrium classification

Nonlinear interactions:

Conflict models, competition models, isoclines, linearization and stability analysis

Physical systems:

Potential energy landscapes, conserved quantities, orbits

Additional models:

Predator-prey systems, transport models

Learning Objectives and Instructor Expectations

Please read the official course outline in PDF format or PS format.

Although the subject matter of Introduction to Continuous 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. Applications will be emphasized.

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Grading

Tutorials