**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)