M.Sc. Physics (I Semester)
Paper I: MATHEMATICAL PHYSICS
Unit1
Beta & Gamma functions -definition, relation between them- properties' Legendre's Differential equation: The Power series Solution-Legendre Functions ofthe first and second kind -Generating Function- Rodrigue's formula- orthogonal Properties - Recurrence Relations-Physical applications. Associated Legendre equation, orthogonat properties ofAssociated Legendre's function. Bessel's Differ-ential Equation: Power series Solution -Bessel Functions ofFirst and Second kind- Generating Function -Orthogonal Properties -Recurrence Relations- Physical applications
Unit-II
Hermite Differential Equation : Power series Solution-Hermite polynomials - Generating Function-Orthogonality -Recurrence relations -Rodrigues formula- Physica[ applications. Laguerre Differentiai equations: The Power series Solution-Cenerating Function- Rodrigue's formula- Recurrence Relations, Orthogonal Properties- - Physical applications'
Unit-III
lntegral Transforms: Laplace transforms definition- properties-Derivative ofLaplace traniorm- Laplace transform ofa derivative -Laplace transform ofperiodic functionevaluation of Laplace transforms-lnverse Laplace transforms-properties- evaluation of lnverse Laplace transforms- elementary function method- Partial fraction method- Solution of ordinary diiferential equation by using Laplace transformation method-Fourier series- evaluation of Fourier coeffrcients- problems-Fourier Transforms- infinite Fourier Transforms-Finite Fourier Transforms-Properties- probl ems.
Unit-IV
Complex variables: Function of complex number- definition-properties, analytic functionCauchy -Riemann conditions-polar form-problems, Cauchy's integral theorem, Cauchy's integral formula- problems ,Taylor's Series-Laurent's expansion-Problems, Calculus of Residues, cauchy's Residue theorem, Evaluation of Residues, Evaluation of contour integrals.
Unit-V
TenSor Analysis: Introduction- Contravariant, Covariant and mixed tensors - Rank ofa tensor - symmetric and anti-symmetric tensors - Invariant tensors, Addition and multiplication oftensors, Outer and inner products- contraction oftensors and quotient law.