MSM1104 - Mathematical Modelling

HNGU M.SC. MATHEMATICS SEMESTER - I

 MSM1104 – MATHEMATICAL MODELLING

Unit 1: 

• Introduction to the subject, its scope and limitation,
• classification of models.
• Dimensional Homogeneity,
• Technique of dimensional analysis,
• An arithmetic model of Gravity,
• Simple population growth model,
• Logistic population growth model,
• Geometric interpretation of logistic growth function.

Unit 2: 

• Two Species Population Models: Prey–Predator models for population dynamics,
• Geometric interpretation and stability of Prey-Predator model,
• Competition model,
• EpidemicModels,
• Simple deterministic model,
• SIS Model,
• Epidemic Models with constant number of carriers,
• Epidemic model with removal.

Unit 3:

• Diffusion and Glucose in the Blood stream,
• Model for diabetes Mellitus,
• Genetics Models,
• Hardy-Weinberg law model for genetics,
• Genetics model for Blood groups.

Unit 4: 

• Traffic Models,
• Macroscopic Highway traffic model,
• continuum hypotheses and the fundamental diagram, 
• linear-car-following models.

Download Reference Books:

Note:The course is roughly covered by the following two books:

• J. N. Kapur, Mathematical Modeling, Wiley Eastern Ltd., 1988.
• J. N. Kapur, Mathematical Models in Biology and Medicine, East–West press Pvt. Ltd., 1992.

1. Braum, Colemem & Drew, Differential Equation Models, Springer–Verlag, 1983.

2. Martin Braun, Differential Equation and their applications, Springer-Verlag, 1977.

3. Dym & Ivey, Principles of Mathematics Modeling, Academic press – 1980.

4. Lucas & Roberts, Discrete and system models, Springer Verlag, 1983.

5. Haberman, Mathematical Model, Prentice–Hall Inc., 1977.

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