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6th June 2016, 11:52 AM
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Join Date: Aug 2012
Re: University of Calcutta M Sc Physics Syllabus

The Syllabus for M.Sc. Course in Physics offered by University of Calcutta is as follows:

PHY 411: Mathematical Methods
1. Complex variables (13)
Recapitulation : Complex numbers, triangular inequalities, Schwarz inequality. Function of a complex
variable — single and multiple-valued function, limit and continuity; Differentiation — CauchyRiemann
equations and their applications; Analytic and harmonic function; Complex integrals,
Cauchy’s theorem (elementary proof only), converse of Cauchy’s theorem, Cauchys Integral Formula
and its corollaries; Series — Taylor and Laurent expansion; Classification of singularities; Branch point
and branch cut; Residue theorem and evaluation of some typical real integrals using this theorem.
2. Theory of second order linear homogeneous differential equations (6)
Singular points — regular and irregular singular points; Frobenius method; Fuch’s theorem; Linear
independence of solutions — Wronskian, second solution. Sturm-Liouville theory; Hermitian operators;
Completeness.
3. Inhomogeneous differential equations : Green’s functions (3)
4. Special functions (3)
Basic properties (recurrence and orthogonality relations, series expansion) of Bessel, Legendre, Hermite
and Laguerre functions.
5. Integral transforms (3)
Fourier and Laplace transforms and their inverse transforms, Bromwich integral [use of partial fractions
in calculating inverse Laplace transforms]; Transform of derivative and integral of a function; Solution
of differential equations using integral transforms.
6. Vector space and matrices (7)
Vector space: Axiomatic definition, linear independence, bases, dimensionality, inner product; GramSchmidt
orthogonalisation.
Matrices: Representation of linear transformations and change of base; Eigenvalues and eigenvectors;
Functions of a matrix; Cayley-Hamilton theorem; Commuting matrices with degenerate eigenvalues;
Orthonormality of eigenvectors.
7. Group theory (10)
Definitions; Multiplication table; Rearrangement theorem; Isomorphism and homomorphism; Illustrations
with point symmetry groups; Group representations : faithful and unfaithful representations,
reducible and irreducible representations; Lie groups and Lie algebra with SU(2) as an example.
8. Tutorials (15)

University of Calcutta M Sc Physics Syllabus





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