AMAT 42783 : Advanced Mathematical Modeling

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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:

  1. Kapur, J.N., Mathematical Modeling, New Age International. (2015).
  2. A., Bender, An introduction to Mathematical Modeling, Courier Corporation, 2012
  3. Richard Haberman, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow. SIAM ,(1998)
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