programme

Mathematical Modelling

Home/ Mathematical Modelling
Course TypeCourse CodeNo. Of Credits
Foundation ElectiveSUS1MA5414

Semester and Year Offered: Winter 2018

Course Coordinator and Team: Kranti Kumar, Balchand Prajapati

Email of course coordinator: kranti@aud.ac.in

Pre-requisites: Probability and Statistics and Ordinary Differential Equations

Aim:

This course has been designed keeping in mind the students who have already been exposed to MA507 and MA510. The main objective of this course is to provide an introduction to modelling and simulation and how to model, solve and interpret real life problems using different Mathematical perspectives.

Course Outcomes:

After completing this course, students will be able

  1. to understand concept of modelling and simulation
  2. to construct mathematical models of real world problems
  3. to solve the mathematical models using mathematical techniques and with the help of Excel sheets.

Brief description of modules/ Main modules:

The following topics will be covered in the course under the three main modules as described below.

  • Interacting Population Model and Phase Plane Analysis An epidemic model of influenza, Predictor and Prey Model, Competing Species, Model of Battle, Phase Plane Analysis of Predictor and Prey, epidemic and Battle Models.
  • Deterministic Dynamical Programming Two Puzzles, A network problem, shortest path, inventory problem, Resource Allocation problem, Knapsack problem, Formulating Dynamical programming problem
  • Simulation Basic Terminology, Discrete Event Simulation, Random number with Monto Carlo Simulation, Example of Monto – Carlo Simulation, Simulation for continuous random variables
  • Lab exercises (MS Excel)
  1. Solving Knapsack problems
  2. Solving inventory problems
  3. Solving Resource allocation problems

Assessment Details with weights:

S.No

Assessment

Date/period in which Assessment will take place

Weightage

1

Class test                     

Second/third week of February, 2018

10%

2

Mid Semester Exam

As per AUD Academic Calendar

25%

3

Tut/LabAssessment

Throughout the semester

20%

4

Presentation/ Viva

First/Second week of April, 2018

10%

5

End Semester Exam

As per AUD Academic Calendar

35%

 

Reading List:

  • Wayne. L. Winston, Probability Models, India Edition, Cengage Learning, reprint 2009, ISBN-13: 978-81-315-0901-2.
  • Belinda Barnes and Glenn Robert Fulford,Mathematical modelling with Case Studies A Differential Equations Approach Using Maple and matlab, Second Edition (Special indian Edition), CRC Press Taylor and Francis, ISBN-13: 978-1-4200-8348-4.
  • Daniel P. Maki, Maynard Thompson, `Mathematical Modeling with Computer Simulation', India Edition, Cengage Learning, 2011ISBN-13: 978-81-315-1286-9.
  • J N Kapur, `Mathematical Modeling', New Age Publishers, 2005, ISBN: 81-224-0006-X.

ADDITIONAL REFERENCE: