Course Unit Code : AMAT 42783
Course Title : Advanced Mathematical Modeling
Pre-requisites : AMAT 41763
Learning outcomes:
Upon successful completion of the course unit the student will be able to:
- explain how the general principals arise in the context of Mathematical Modeling
- analyze some existingmathematical models and construct simple models for real world situations.
- explain and apply the basic concepts of Mathematics and their uses in analyzing and solving real-world problems
Course Content:
Introduction to Modeling: Philosophy of modeling, Modeling Methodology, Problem formulation, Mathematical Description, Analysis, Interpretation
Mathematical Modeling Using Ordinary Differential Equations: Classification of ODE, Equilibrium points, Qualitative analysis of equilibrium points.
First order Differential Equations: Mixing, chemical reactions, Population models: Logistic growth model, Harvesting models, Traffic Dynamic models: Microscopic and macroscopic models
System of Differential equations: Interacting population models (Predator –Prey models, Competition models), Compartment models (Dynamic of infectious disease, Age structured models, Reaction kinetics)
Mathematical Modeling Using Difference Equations: First order difference equations, Equilibrium points, asymptotic stability of equilibrium points, System of linear difference equations: Autonomous systems, Discrete analogue of Putzer algorithm, Jordan form, linear periodic systems
Applications: Markov chains, Population dynamics, Trade models, Age classes, Business cycle models.
Group Project: Mathematical model formulation for a real world problem
Method of teaching and learning : A combination of lectures and tutorial discussions
Assessment : Continuous assessment and/or end of course unit examination
Recommended Textbook:
- Kapur, J.N., Mathematical Modeling, New Age International. (2015).
- A., Bender, An introduction to Mathematical Modeling, Courier Corporation, 2012
- Richard Haberman, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow. SIAM ,(1998)