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Modelling and Simulation [1]

Paper Code: 
25MAT425(B)
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
1. Provide knowledge about modelling and simulation 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: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

25MAT

425(B)

 

 

 

Modelling and Simulation

 (Theory)

 

 

 

CO196: Classify Systems and explore modelling Process, advantages and disadvantages of simulation and modelling.

CO197: Evaluate linear and non-linear growth and decay models.

CO198: Analyze compartment models. Evaluate model validity and verify through Model V&V. CO199: Explore mathematical modeling through ordinary differential equations, partial differential equations.

CO200: Evaluate the basic concepts of simulation languages and stochastic processes and also be able to develop proficiency in discrete system simulation techniques.

CO201: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions,  Topic  presentation, Assigned tasks

 

 

Quiz, Class Test, Individual projects,

Open Book Test, Continuous Assessment, Semester End Examination

 

 

 

(Note: Non-Programmable scientific calculator up to 100 MS is permitted)
 
Unit I: 
Introduction to modelling and simulation:
15.00
Definition of System, Type of System: Discrete system and continuous system, classification of systems, Modelling process, Advantage and disadvantage of simulation, Classification and limitations of mathematical models and its relation to simulation.
 
Unit II: 
Modelling through differential equation:
15.00

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: 
Compartment models:
15.00

 One-Compartment models and Two-Compartment models, Equilibrium solution, Stability analysis, Model validity and verification of models (Model V&V), modelling through graph (in terms of weighted graph, In terms of signed graph, in terms of directed Graph).

Unit IV: 
Mathematical modelling through ordinary differential equation:
15.00
 SI model, SIR model with and without vaccination. Partial differential equation: Mass and momentum balance equations, wave equation.
 
Unit V: 
Concept of Continuous and Discrete Simulation:
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 Modelling, Pergamum Press, 2013.
  • J. N. Kapoor, Mathematical Modelling, 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.
  • B. Singh and N. Agrawal, Bio-Mathematics, Krishna Prakashan, 2023.
 
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: 
2025-2026 [10]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/modelling-and-simulation-2

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/modelling-and-simulation-2
[2] https://nptel.ac.in/courses/112107214
[3] https://nptel.ac.in/courses/112107220
[4] https://nptel.ac.in/courses/103107096
[5] https://nptel.ac.in/courses/110104096 
[6] http://pcleon.if.ufrgs.br/pub/listas-sistdin/MurrayII.pdf
[7] https://www.jhuapl.edu/Content/techdigest/pdf/V16-N01/16-01-Menner.pdf
[8] https://www.vssut.ac.in/lecture_notes/lecture1428910921.pdf
[9] https://ptolemy.berkeley.edu/books/Systems/PtolemyII_DigitalV1_02.pdf 
[10] https://maths.iisuniv.ac.in/academic-year/2025-2026