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MATHEMATICAL METHODS IN PHYSICS
- The main objective of this course is to impart knowledge about various mathematical tools employed to study physics problems.
- 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.
- 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.
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Assessment Strategies |
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Paper Code |
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PHY 122 |
Mathematical Methods in Physics
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After completion of the course the student 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
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Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations |
Contravariant and covariant tensor, Jacobian, pseudo tensors , Algebra of tensors, Metric tensors, Associated tensors, Christoffel symbols, transformation of Christoffel symbols.
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.
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
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.
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.
- “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.
