Modelling and Simulation

Paper Code: 
MAT425 B
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. 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):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

MAT 425B

 

 

 

Modeling and Simulation

 (Theory)

 

 

 

The students will be able to –

 

CO194: Analysis 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.

CO195: Demonstrate the population model, Prey Predator Model and Competition model with application.

 CO196: Analysis the stability of system, modelling through graph and Verification and Validation of model.

CO197: Determine SIR, SIS model for epidemic and reproduction number which is used to control epidemics.

CO198: Construct model of differential equation using real life problem and solve them.

CO199: Define the types of simulations, simulation languages, pseudo-random numbers, Marcov chain and variants from different probability distributions.

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

 

 

 

(Note: Non-Programmable scientific calculator up to 100 MS is permitted)

 

 

Unit I: 
I
15.00
Introduction to modeling and simulation, Definition of System, Type of System: Discrete system and continuous system, classification of systems, Modeling process, Advantage and disadvantage of simulation, Classification and limitations of mathematical models and its relation to simulation.
 
Unit II: 
II
15.00

 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.

 
Unit III: 
III
15.00
Compartment models:  One-Compartment models and Two-Compartment models, Equilibrium solution, Stability analysis, Model validity and verification of models (Model V&V), Modeling through the graph (in terms of a weighted graph, In terms of a signed graph, in terms of directed Graph).
 
Unit IV: 
IV
15.00
Mathematical modeling through ordinary differential equation: SI model, SIR model with and without vaccination. Partial differential equation: Mass and momentum balance equations, wave equation.
 
Unit V: 
V
15.00
Basic concepts of simulation languages, Overview of numerical methods used for continuous simulation, Stochastic Process (Marcov process, Transition probability, Marcov chain, Steady state condition, Marcov analysis), Discrete system simulation (Monte Carlo method, Random number generation).
 
Essential Readings: 
  • 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.
References: 
  • 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.
 
Academic Year: 
2022-2023
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