MAT 368E - Mathematical Modeling

Course Objectives

1. To teach fundamental concepts and approaches of the mathematical modelling.
2. By considering some problems of the engineering, industry and life, to teach investigate and solve as a mathematical problem.
3. To teach interpretation of model results and how to make improvements in the model.

Course Description

Principles, scale and dimension analysis. Mechanical vibration; linear oscillator and nonlinear pendulum. Populations models; discrete one-species models, predatory-prey models. Lotka-Volterra equations. Traffic flow models; traffic flow, density and conservation laws, velocity-density relationship and density waves. Mathematical epidemiology; Kermack-McKendrick SIR epidemic model, the SIR model with demography. The air quality modelling; advection equation, advection diffusion equation, the solutions and the stability analysis. Mathematical modelling of tumor growth.