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Mathematical Physics
Course Objectives:
This course will enable the students to acquaint the students with different types of coordinate systems, tensors, four vectors etc. The students will also learn to make Fourier analysis of complex functions and use various numerical methods for solving different types of Physical Science problems.
Course Outcomes (COs):
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Course |
Learning outcome (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
Paper Title |
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DPHY501 (C) |
Mathematical Physics (Theory) |
The students will be able to – CO52: Evaluate the gradient, divergencet and curl of various functions in orthogonal curvilinear coordinate system.
CO53: Apply the concept of tensors in physical problems.
CO54: Gain the knowledge of Four vector notation.
CO55: Apply a range of techniques to solve first & second order partial differential equations.
CO56 : Find the Fourier analysis of periodic functions and apply it to solve physical problems such as vibrating strings etc.
CO57: Solve differential equations using numerical methods.
CO58: Evaluate numerical integration.
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Approach in teaching: Interactive Lectures, Discussion, Power point presentation Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation, Solving numericals |
Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations |
Orthogonal curvilinear coordinate system, scale factors, Expressions for gradient, divergence and curl and their application to Cartesian, Circular Cylindrical and Spherical polar coordinate systems.
Tensors: Coordinate transformations, Transformation of covariant, contra variant and mixed tensors. Addition, subtraction, outer product, contraction and inner product of tensors, Quotient law, Symmetric and antisymmetric tensors, Metric tensor.Dirac delta function and its properties.
Four vector formulation, four-velocity vector, energy-momentum four vector, relativistic equation of motion; invariance of rest mass, orthogonality of four force and four velocity, Lorentz force as an example of four force, transformation of four frequency vector, longitudinal and transverse Doppler’s effect, Compton effect.
Techniques of separation of variables and its application to the following boundary value problems (i) Laplace’s equation in three-dimensional Cartesian coordinate system – line charge between two earthed parallel plates, (ii) Helmholtz equation in circular cylindrical coordinates-Cylindrical resonant cavity, (iii) Wave equation in spherical polar coordinates-the vibrations of a circular membrane, (iv) Diffusion equation in two dimensional Cartesian coordinate system-heat conduction in a thin rectangular plate.
Introduction, Fourier series and coefficients, functions with point of discontinuity, Expansion of periodic functions in a series of sine and cosine functions and determination of Fourier coefficients. Complex representation of Fourier series. arbitrary period, even and odd functions, half range expansion, Application. Summing of Infinite Series, Parseval’s theorem.
Introduction, Finite-Difference Operators, Differential Operator related to the Difference Operator, Truncation error, Numerical interpolation, Roots of equations, Initial-value problems –Ordinary Differential equations: Taylor’s method, Euler’s method and direct method. Trapezoidal and Simpson’s rule for numerical integration.
1.“Mathematical Methods” , Potter and Goldberg, Prentice Hall of India (1998).
2.“Mathematical methods in Physics”, D.Biswas, New Central Book Agency (P) Ltd.
3.“Introduction to Mathematical Physics”, Michael T. Vaughn, Wiley India Pvt Ltd.
References:
1.“Applied Maths for Engineers and Physicists”,Pipes and Harvill, McGraw Hill.
2.“Advanced Engineering Mathematics”, Ervin Kreyzig 5th Edition, Wiley Eastern Ltd.
3.“Numerical Methods”, S. Balachandra Rao, C.K. Shantha, University Press, 1992.
4.“Mathematical Physics”,Ellgnine Butkon, Addisson Wiesley.
5.“Mathematical Physics”,Gupta, Vikas Publishing House.
6. Mathematical Methods for Physicists: Arfken, Weber, 2005, Harris, Elsevier.
7. Fourier Analysis by M.R. Spiegel, 2004, Tata McGraw-Hill.
8. Mathematics for Physicists, Susan M. Lea, 2004, Thomson Brooks/Cole.
9. An Introduction to Ordinary Differential Equations, Earl A Coddington, 1961, PHI Learning.
10.Differential Equations, George F. Simmons, 2006, Tata McGraw-Hill.
11.Essential Mathematical Methods, K.F. Riley and M.P. Hobson, 2011, Cambridge University Press
12.Partial Differential Equations for Scientists and Engineers, S.J. Farlow, 1993, Dover Publications.
13. Mathematical methods for Scientists and Engineers, D.A. McQuarrie, 2003, Viva Books.
