Computational Physics course at the University of Delhi Amitabha Mukherjee Department of Physics and Astrophysics and Centre for Science Education and Communication University of Delhi Workshop on the Teaching of Computational Physics Bombay, 14 March 2009

Outline Background of the course Structure and placing Syllabus Experiences of teaching In retrospect

Background of the course Compulsory Computer Lab in M.Sc. (Prev.) No impact of Prev. lab on teaching of Physics courses “The design of the structure of the MSc Final courses was guided by the desire to have a mix of what additional numerical skills students would require for their research plus some interesting numerically intensive physics that could be done by students with the skills they had picked up during the Previous course work.”

Structure and placing A 2-semester optional course Available to students in the Theory stream in M.Sc. (Final) Marks: 100, out of 500 for the year Unique among Theory courses in having a Lab component Taught by 2 teachers in each semester

People involved Patrick Das Gupta Shobhit Mahajan Amitabha Mukherjee Vijaya S Varma

Syllabus - I Overview Symbolic Manipulation Signal Processing and Data Analysis Nonlinear Equations

Syllabus - II Numerical Solution of Partial Differential Equations Numerical Solution of Partial Differential Equations Numerical Solution of Integral Equations Numerical Solution of Integral Equations Monte Carlo Techniques Forward

Symbolic Manipulation Arbitrary precision arithmetic, algebraic operation, differentiation, integration, matrix operations and simultaneous equations. Application to the calculation of scattering cross sections, elements of Riemann and Weyl tensors, etc. (12 Lectures) Back to Syllabus

Signal Processing and Data Analysis Fast transforms (Fourier and Wavelet), random noise and signal, white and coloured noise, power spectrum. Convolution, auto-correlation and cross- correlation, matched filtering techniques. The maximum entropy method. Application to atmospheric physics, pulsars, etc. (12 Lectures) Back to Syllabus

Nonlinear Equations Maps, flows, routes to chaos – period doubling, intermittency and strange attractors. Lyapunov exponents, fractal dimensions, analysis of time series, control of chaos. Application to climate modelling, chaotic quantum optic systems, etc. (12 Lectures) Back to Syllabus

Numerical Solution of Partial Differential Equations 1st and 2nd order, linear and nonlinear differential equations. Solution by the method of iteration, relaxation, Fourier and cyclic reduction, and the Rayleigh-Ritz method. Application to diffusion of dopant in a semiconductor, wave equation in a coaxial cable, vibrating strings and membranes, Poisson equation, etc. (12 Lectures) Back to Syllabus

Numerical Solution of Integral Equations Fredholm equation of the 2 nd kind, Volterra equation, integral equations with singular kernels. Linear regularisation method, the Backus- Gilbert method. Application to the non- relativistic Coulomb problem, nuclear scattering, etc. (12 Lectures) Back to Syllabus

Monte Carlo Techniques Evaluation of single- and multi- dimensional integrals, optimisation problems, simulations of many-particle systems. Applications to statistical mechanics, Metropolis algorithm etc. (12 Lectures) Back to Syllabus

First 3 years: 6-7 students, good response Some students have become professional physicists Sharp drop after 3 years: 1-2 students Not offered since 2003 Experiences of teaching

In retrospect Software costs were a limitation, e.g. choice of REDUCE Commercial purchase of software needed Familiarity with packages should be built in, less emphasis on writing code

In retrospect - II Possible reason for drop in students: Too much work compared to other optional papers Not enough physics learnt Any new course should address this core issue

Thank you

Contact information Amitabha Mukherjee Centre for Science Education and Communication ARC building, 2 nd floor (opp Khalsa College), Delhi University, Delhi Phone: