Computational Physics

Syllabus

Computational Physics is considered by many as the Third Pillar of Science along with Theory and Experiment. The course will be focused on Numerical Algorithms, Case Studies in Physics and Computational tools. Namely: 1. Numerical methods in Physics (Linear Algebra, Numerical Integration, Monte Carlo methods, ODEs, PDEs); 2. Case Studies (Heat Equation, Random Walk, Metropolis Algorithm, Wave Equation); 3. Tools and Advanced topics (Programming in Python, Parallel and Grid Computing).

Course Plan:

1. Introduction & course overview
2. Getting acquainted with the computer lab and basic programming
3. Numerical precision and basic numerical analysis (approximation of a function)
4. Linear Algebra
5. Numerical integration and Parallelization
6. Parallel Computing in MPI (Message Passing Interface)
7. Random numbers and Monte Carlo methods
8. Diffusion equation and random walks, Parallel Computation of a steady state heat equation
9. Metropolis algorithm and studies of phase transitions
10. Ordinary differential equations
11. Partial differential equations
12. Wave equation in one and two dimensions
13. Students Projects presentations

Sources:

1. Computational Physics by Morten Hjorth-Jensen.
2. An Introduction to Computational Physics by Tao Pang, the University of Nevada, Las Vegas. 2nd edition, Cambridge University Press, 2006.
3. Python Scripting for Computational Science by Hans Petter Langtangen, Third Edition, Springer, 2008.

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