General Relativity & Cosmology (Optional Paper)

Paper Code: 
MAT 425A
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Provide a detailed knowledge of  the general relativity and its applications in Cosmology.
  2. Solve the problems and help in research in these broad areas.

 

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

MAT 425A

 

 

 

 

General Relativity & Cosmology

 (Theory)

 

 

 

The students will be able to –

 

CO188: Formulate Einstein field equation for matter and empty space.

 

CO189: Understand the concept of clock paradox in general relativity.

 

CO190: Derive the differential equation for planetary orbit, analogues of kepler's law.

CO191: Derive Schwarzschild interior, exterior metric and their isitropic forms.

CO192: Calculate the Trace of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid.

CO193: Apply the concepts of Einstein tensor, Energy-momentum tensor and its expression for perfect fluid,

 

 

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

 

 

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 graph (in terms of weighted graph, In terms of 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.
  • 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: 
2021-2022
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