P602 – Mathematical methods

Course No: 
  1. Vectors and Tensors (index notation,vector analysis in curvilinear coordinates. Cartesian tensors and four vectors, General tensors).
  2. Review of Linear Algebra with emphasis on applications to physical problems (linear transformations + Matrix representations, Eigen values + Eigen Vectors, Innner product spaces).
  3. Review of complex analysis with applications (Cauchy-Riemann equations, Complex integration, Cauchy theorems, Contour integration, Branch points and branch cuts, Applications to integrals, series etc.)
  4. Hilbert Space methods, special functions (hilbert space, Orthonormal series expansions in Hilbert space especially Fourier series, Special functions
  5. Ordinary and partial differential equations (Analysis of second order OFE’s Sturm-Liouville system, Boundary value problems for Laplace Diffusion (Heat) and wave equations)
  6. Integral transforms, its applications and generalized functions (Laplace and Fourier transform, Dirac delta and other generalized functions, Green’s functions of ODE and PDE)
  7. Group theory (introduction using various groups occuring in physics, its algebra, Representation of groups, Characters)
  8. Probability and Statistics (probability distributions, Stochastic processes like Brownian motion, Error analysis for experiments, Statistical inference)
Reference Books: 
  1. Arfken and Weber, Mathematical Methods
  2. C.Harper, Mathematical methods
  3. T L Chow, Mathematical method for physicists.
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