AMAT 32323: Mathematical Modeling

Course Unit Code : AMAT 32323

Course Title           : Mathematical Modeling

Pre-requisites         : PMAT 22282

Learning outcomes:

Upon successful completion of the course unit the student will be able to:

• explain how the general principles arise in the context of mathematical modeling

• analyze existing mathematical models using ordinary differential equations

• formulate simple ODE models for real world problems

• solve system of ordinary differential equations

• analyze the qualitative behavior of mathematical models

•  identify the solutions of difference equations

• solve system of linear difference equations using Putzer algorithm and Jordan form.

Course Content:

Introduction to Mathematical Modeling: 

• Philosophy of modeling, Modeling Methodology, Problem formulation, Mathematical Description, Analysis, Interpretation.

Mathematical Modeling Using Ordinary Differential Equations: 

• Classification of ODE, 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), Qualitative analysis of models.

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.

Method of Teaching and Learning : A combination of lectures and tutorial discussions.

Assessment : Based on tutorials, tests and end of course examination.

Recommended Textbook:

1. Kapur, J.N. (2015). Mathematical Modeling, New Age International.

2. Bender, A. (2012). An introduction to Mathematical Modeling, Courier Corporation.

3. Haberman, R. (1998). Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow. SIAM.

4. Allen, L. (2006). An Introduction to Mathematical Biology, Pearson.

5. Elaydi, S. (2005). An Introduction to Difference Equation, Springer.