Coming soon
Mathematical Physics
This course will enable the students to:
- Impart knowledge about various mathematical tools to study physics problems.
- Familiarize with different types of tensors and their algebra, Fourier and Laplace transforms.
- Use 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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Learning outcomes (at course level) |
Learning and teaching strategies |
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Course Code |
Course Title |
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24PHY 122 |
Mathematical Physics (Theory)
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CO7: Extend the knowledge of tensors acquired at Graduation level and apply it to different types of tensors. CO8:Demonstrate a detailed mathematical understanding of tensors in solving various physical problems. CO9: Apply the concept of group theory to various physical systems. CO10:Investigate wave equations and diffraction theory using Fourier Transforms. CO11: Develop an understanding of Laplace transforms to solve differential equations. CO12: Contribute effectively in course-specific interaction. |
Approach in teaching: Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration.
Learning activities for the students: Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation, Solving numerical, problems |
Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations |
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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 and their properties, Fourier transform of Derivatives, Solution of wave equation as an application, Convolution theorem, 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.
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