#2
 
 
Re: University of Calcutta Msc Physics
As you want to take admission in University of Calcutta to do Msc Physics course , and asking for its syllabus to do compare with other university syllabus, so on your demand I am providing same for you: PHY 411: Mathematical Methods 1. Complex variables (13) Recapitulation : Complex numbers, triangular inequalities, Schwarz inequality. Function of a com plex variable — single and multiplevalued function, limit and continuity; Differentiation — Cauchy Riemann 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. SturmLiouville 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; Gram Schmidt orthogonalisation. Matrices: Representation of linear transformations and change of base; Eigenvalues and eigenvectors; Functions of a matrix; CayleyHamilton theorem; Commuting matrices with degenerate eigenvalues; Orthonormality of eigenvectors. 7. Group theory (10) Definitions; Multiplication table; Rearrangement theorem; Isomorphism and homomorphism; Illustra tions 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 
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