Transcript Careers in Physics

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
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Background of the course
Structure and placing
Syllabus
Experiences of teaching
In retrospect
Background of the course
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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
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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
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Patrick Das Gupta
Shobhit Mahajan
Amitabha Mukherjee
Vijaya S Varma
Syllabus - I
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Overview
Symbolic Manipulation
Signal Processing and Data Analysis
Nonlinear Equations
Syllabus - II
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Numerical Solution of Partial Differential
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 crosscorrelation, 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 2nd kind,
Volterra equation, integral equations
with singular kernels. Linear
regularisation method, the BackusGilbert method. Application to the nonrelativistic Coulomb problem, nuclear
scattering, etc.
(12 Lectures)
Back to Syllabus
Monte Carlo Techniques
Evaluation of single- and multidimensional integrals, optimisation
problems, simulations of many-particle
systems. Applications to statistical
mechanics, Metropolis algorithm etc.
(12 Lectures)
Back to Syllabus
Experiences of teaching
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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
In retrospect
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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
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Possible reason for drop in students:
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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, 2nd floor (opp Khalsa College),
Delhi University, Delhi 110007
Phone: 27666599
Email: [email protected],
[email protected], [email protected]