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15th November 2017, 11:53 AM
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Join Date: Aug 2012
Re: Mahatma Gandhi University Faculty of Applied Science

The M Sc Physics Program Syllabus offered by School of Pure & Applied Physics of Mahatma Gandhi University, Kerala is as follows:

UNIT I
Vector spaces and vector analysis (10 hours) Linear vector spaces, Schmidt orthogonalisation, linear operators, dual space, ket and bra notation, Hilbert space, Metric space, Function spaces, Riesz Fisher theorem (no proof),basis, orthogonal expansion of separable Hilbert spaces, Bessel inequality, Parsevals formula, Orthogonal curvilinear coordinates-gradient, divergence, Curl and Laplacian. Evaluation of line, surface,volume integrals.

UNIT II
Differential geometry (15hours) Definition of tensors, Metric tensor, One-form, metric tensor as a Mapping of vectors into one form. Covariant, Contravariant, and mixed tensors. Differentiable manifolds and tensors, Riemannian transport, geodesics, Christoffel symbols and curvature, Riemann curvature tensor, Ricci tensor and Ricci scalar: their definitions and properties , Bianchi identities.

UNIT III
Sturm-Liouville theory, special functions and their differential equations (15 hours) Frobenius method for solving second order ordinary differential equations with variable coefficients. Bessel ,Legendre, Hermite equations. Recurrence relations, generating functions and Rodrigues formulae for the Bessel, Legendre and Hermite functions Linear differential operators, adjoint operators, Greens identity, eigen values and eigen functions, Sturm-Lioville operators and eigen values and eigen functions

UNIT IV
Greens functions (20 hours) Dirac delta functions-properties and representations, Definitions and physical significance of Greens functions, Translational invariance, eigen function expansion of Greens function, Greens function for ordinary differential operators, first order linear differential operators and second order linear differential operators.(Eg. Forced harmonic oscillator) Greens functions for partial differential operators, Laplace diffusion equation and wave equation operators, solution of boundary value problems using greens function for Laplace, Poisson and wave equations.

References
1. Mathematical methods in classical and quantum physics- T. Das and S.K. Sharma, University Press (1998)
2. Theory and problems of vector analysis- M. Spiegel, Schaum Out line series, McGraw Hill Book Company.
3. A first course in general relativity- B.F.Schutz, Cambridge university press (1985) 4. Mathematical methods for physicists- G.B. Arfken and ,H.T.Weber


M Sc Physics Syllabus School of Pure & Applied Physics MG University, Kerala






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