### PH 5O5O Mathematical Physics-II

#### Course Details

** Course Contents : **

Complex Variables Analytic functions of a complex variable. Cauchy-Riemann conditions. Power series. Cauchy?s integral theorem. Conformal mapping.
Singularities: poles, essential singularities. Residue theorem. Contour integration and examples. Analytic continuation. Multiple-valued functions, branch points and branch cut integration.
Partial Differential Equations : Partial differential equations in Physics: Laplace, Poisson and Helmholtz equations; diffusion and wave equations. Applications. Integral transforms : Laplace transforms and Fourier transforms. Parsevall?s theorem. Convolution theorem. Applications. Calculus of Variations Functionals. Natural boundary conditions. Lagrange multipliers. Rayleigh-Ritz method.
Group theory : Elements of group theory. Discrete groups with examples. Contionuos groups (Lie groups) [rotation group in 2 and 3 dimensions, U(1) and SU(2)]. Generators.
Representations, Character tables for some point groups and the orthogonality theorem.

#### Course References:

** References: **

1. G. Arfken and H.J. Weber, Mathematical Methods for Physicists, Academic Press, 6th Edition, Indian Edition, (2005).
2. P. Dennerey and A. Kryzwicki, Mathematics for Physicists, Dover (Indian Edition), (2005).
3. K.F. Riley, M.P. Hobson and S.J. Bence, Mathematical Methods for Physics and Engineering, Cambridge University Press (Cambridge Low-priced Edition) (1999).
4. Schaum?s outline series, McGraw Hill (1964): (i) Complex Variables, (ii) Laplace Transforms, (iii) Group Theory.
5. M. Boas, Mathematical Methods in Physical Sciences, 2nd Edition, Wiley International Edition, (1983).
6. E. Kreyszig, Advanced Engineering Mathematics, Wiley Eastern, 5th Edition, (1991).
7. L.A. Pipes and L.R. Harwell, Applied Mathematics for Engineers and Physicists, McGraw-Hill, (1995).
8. M.Artin, Algebra, Prentice-Hall India, (2002).
9. I.N. Sneddon, The Use of Integral Transforms, Tata McGraw Hill, (1985).
10. D.H. Sattinger and O.L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics, Springer, (1986).
11. M. Tinkham, Group Theory and Quantum Mechanics, Dover (2003).