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.