MODELING AND SIMULATION (Optional Paper)
- Provide knowledge about Modeling and Simulation (M & amp; S) which is the use for different models (e.g., physical, mathematical, or logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop data utilized for managerial or technical decision making.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
Paper Title |
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MAT 425B
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Modeling and Simulation (Theory)
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The students will be able to –
CO155: Students will get ideas about the individual-based models of infectious diseases. These models allow us to incorporate stochastic effects, and individual-scale detail in ways that cannot be captured in more traditional models. CO156: Students review a framework based on directed random networks that unifies a range of individual-based models in closed populations, simplifying their analysis. We then show how this framework provides a new and potentially useful perspective on the design of vaccination strategies. Student will also get idea about reproduction number which is used to control epidemics. CO157: Students get ideas about The types of simulations, simulation languages, pseudo-random numbers, Marcov chain and variants from different probability distributions. CO158: Students learn about the systems and its type, mathematical modeling, simulation there advantages and drawbacks. CO159: Students learn how to do modelling through graph, LPP. |
Approach in teaching: Interactive Lectures, Discussion, Power Point Presentations, Informative videos Learning activities for the students: Self learning assignments, Effective questions, presentations, Field trips |
Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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(Note: Non-Programmable scientific calculator up to 100 MS is permitted)
Modeling through differential equation: Linear growth and decay models, Nonlinear growth and decay models, Logistic model, Basic model relevant to population dynamics (Prey-Predator model, Competition model), Volterra’s principle.
Compartment models:One-Compartment model and Two-Compartment models, Equilibrium solution, Stability analysis, Model validity and verification of models (Model V&V), Modeling through graph (in terms of weighted graph, In terms of signed graph, in terms of directed Graph).
Mathematical modeling through ordinary differential equations: SI model, SIR model with and without vaccination, Partial differential equation: Mass and momentum balance equations, wave equation.
Basic concepts of simulation languages, Overview of numerical methods used for continuous simulation, Stochastic Process (Marcov process, Transition probability, Marcov chain, Steady state condition, Markov analysis), Discrete system simulation (Monte Carlo method, Random number generation).
- D. N. P. Murthy, N. W. Page and E. Y. Rodin, Mathematical Modeling, Pergamum Press, 2013.
- J. N. Kapoor, Mathematical Modeling, Wiley Eastern Ltd., 2015
- P. Fishwick, Simulation Model Design and Execution, PHI, 1995.
- Brian Albright, Mathematical Modeling with Excel, Jones & Bartlett, 2012.
- A. M. Law and W. D. Kelton, Simulation Modeling and Analysis, McGraw-Hill, 2007.
- J. A. Payne, Introduction to Simulation, Programming Techniques and Methods of Analysis, Tata McGraw Hill Publishing Co. Ltd., 1988.
- V.P. Singh, System Modeling & Simulation, New Age International Publishers, 2009.
