Details of PH4102 (Autumn 2012)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
PH4102 Advanced Mathematical Methods Ananda Dasgupta

Syllabus
Recapitulation :

Vector Spaces, Matrices, Eigen value equations, Properties of Orthogonal, Hermitian and Unitary matrices, Gram-Schmidt orthogonalization procedure, Schwartz inequality and application, Summation of Series and their convergence.


Complex Variable Theory:

Residue Theorem, Evaluation of Integrals, Summation of series through contour integration method, Saddle point approximation scheme and application to WKB approximation , Conformal transformation, Multi valued functions.


Differential Equations :

Solution of first order differential equations and applications, hypergeometric and confluent hypergeometric equations and their singularity structure, series solutions, Orthogonal polynomials and generating functions, Recurrence relations, Solution of Bessel equation, Airy function, Application to WKB approximation, Greens function and its applications.

Group Theory :

Basics, finite groups, representations, irreducibility, characters, applications of finite groups, conntinuous groups, Lie groups and algebra, applications to particle physics.

Differential geometry :

Manifolds, tangent spaces, covariant derivatives, connection, curvature, applications.

Basics of topology :

Topological spaces, continuity, basic notions of homotopy and homology, applications to physics.



References

  1. J.Matthews and R.L. Walker, Mathematical Methods of physics, Benjamin (1970)

  2. G.B. Arfken, H.J. Weber and F.Harris, Mathematical Methods for Physicists, Academic Press (2005)

  3. M. Nakahara, Geometry, Topology and Physics, Taylor and Francis (2003)

  4. C. Nash and S. Sen, Topology and geometry for physicists, Dover (2011)

  5. S. Mukhi and N. Mukunda, Lectures on Advanced Mathematical Methods for Physicists, World Scientific, (2010)







Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 MS 7 Not Allowed
4 RS 1 Not Allowed