MATHEMATICAL METHODS IN PHYSICS

Paper Code: 
PHY 122
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to
  1. The main objective of this course is to impart knowledge about various mathematical tools employed to study physics problems.
  2. This course will familiarize students with a range of mathematical methods. They will study different types of tensors and their algebra, Christoffel’s symbol, Equation of Geodesic and application of tensors to various problems of Physics, Fourier and Laplace transforms.
  3. The student will learn significance of point groups and space groups and their relevance in the study of condensed matter Physics, in particular Crystal Physics.

Course

Learning outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

PHY 122

Mathematica

The students will be able to –

CO 6: Further extend the knowledge of tensors acquired at Graduation level, through learning of their symmetric and antisymmetric nature, contravariant, covariant and mixed tensors and their transformation properties , physical examples of tensors such as stress tensor, strain tensor etc.

 

CO 7: Learn the equation of Geodesic and use it to derive Ricci’s theorem.

 

CO 8: Understand elementary group theory, i.e., definition and properties of groups, subgroups, Homomorphism, isomorphism, normal and conjugate groups, representation of groups, Reducible and Irreducible groups. Crystallographic point groups, reciprocal lattice etc. and to use it to various situations in physical systems.

 

 

CO 9: Evaluate the Fourier transform, the inverse Fourier transform and their applications in physical problems.

 

CO 10: Solve various differential equations using Laplace and inverse Laplace transforms.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration.

 

 

 

 

 

 

 

 

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation, Solving numerical, problems

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations

 

12.00
Unit I: 
I
Contravariant and covariant tensor, Jacobian, pseudo tensors , Algebra of tensors, Metric tensors, Associated tensors,  Christoffel symbols, transformation of Christoffel symbols.
 
11.00
Unit II: 
II
Equation of Geodesic, Covariant differentiation, Ricci's theorem, Divergence, Curl and Laplacian in tensor form, Stress and Strain tensors, Hooke's law in tensor form, Lorentz Covariance of Maxwell equation.
 
13.00
Unit III: 
III
Group of transformations, (Example: symmetry transformations of a square), Generators of a finite group, Normal subgroup, Direct product of groups, Isomorphism and Homomorphism, Representation theory of finite groups, Invariant subspace and reducible representations, irreducible representations, Crystallo-graphic point groups, Irreducible representation of  C4ν, Translation group and the reciprocal lattice. 
 
12.00
Unit IV: 
IV
Development of the Fourier integral from the Fourier series, Fourier and inverse Fourier transform, Fourier transform of Derivatives, Solution of wave equation as an application, Convolution theorem, intensity in terms of spectral density for quasi-monochromatic EM waves, momentum representation, Application of Fourier Transform to Diffraction Theory, Diffraction pattern of single and double slits.
 
12.00
Unit V: 
V
Laplace transforms and their properties, Laplace transform of derivatives and integrals of Laplace transform, Laplace convolution theorem, Impulsive function , Application of Laplace transform in solving linear differential equations with constant coefficient, with variable coefficient and linear partial differential equation.
 
 
 

BOOKS RECOMMENDED:

·         “Mathematical physics”, Satya Prakash, Pragati Prakashan.

·         “Mathematical Methods for Physicists”, George Arkfen ,Academic Press.

·         “Applied Mathematics for Engineers and Physicists”, L. A. Pipe and L.R.  Harvill,   McGraw Hill

·         “Mathematical Methods”, Potter and Goldberg ,Prentice Hall of India.

·         “Elements of Group Theory for Physicists: A. W. Joshi (Wiley Eastern Ltd.)

“Vector Analysis”, Schuam Series, Mc Graw Hill.

 

Academic Year: 
2020-2021
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