Syllabus

At least six problems from the following list have to be completed.

Module 1: (6 hours)
1. Interpolation (Lagrange method).
2. Numerical integration (Simpson & Trapezoidal method).

Module 2: (6 hours)
3. Differentiation (Runge-Kutta method).
4. Numerical solution to partial differential equations.

Module 3: (6 hours)
5. Solving Schrödinger equation for quantum harmonic oscillator or square well potential (finite and infinite).
6. Phase-space analysis of non-linear physical systems.

Module 4: (6 hours)
7. Introduction to Machine Learning. Linear regression.
8. Introduction to classical Monte-Carlo (MC) simulation. MC simulation of 2D Ising model.

Module 5: (6 hours)
9. Problems based on Central Limit Theorem.
10. Problems based on Power-law distribution.

Module 6: (6 hours)
11. Protein folding problem using Monte Carlo method.
12. Simulating chemical equilibrium of a gas using random numbers.

To learn the fundamental computational techniques to solve mathematical and physical problems numerically.

To learn development and optimization of the programming skills to study various physical systems.

To learn plotting, visualizing, and analyzing simulation results with an appropriate theoretical physics background.

At the end of the course, students will be able to learn
CO1: Application of numerical techniques to find derivatives, integrations, and solve differential equations.

CO2: Simulations to understand various physical systems.

CO3: Monte Carlo method and its use in magnetic and bio-physics systems.

CO4: Brief idea about machine learning and its applications.

S. C. Chapra, Numerical Methods for Engineers, McGraw Hill Education India Private Limited.

D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press.

R. H. Landau, M. J. Páez, C. C. Bordeianu, Computational Physics: Problem Solving with Computers, Wiley VCH.

S. Koonin and D. Meredith, Computational Physics: Fortran Version, Westview Press.