Computational Physics (Practical) (Second Year/Third Year)

2006 - Present

The use of computers in Physics has grown enormously in the twentieth and twenty-first centuries, to the point where computers play a central role in virtually every new physics discovery. Assuming no previous computer programming experience, the course will introduce the basic ideas and programming skills of computational physics and students will develop their own computer software to solve problems in quantum physics, electromagnetism, biophysics, mechanics, chaos, nonlinear dynamics, mathematical methods in physics, geophysics, spectral analysis and other areas.

This course gives a modern introduction to the basic methods in computational Physics and an overview of the recent progress in scientific computing. Many examples from recent research in Physics and related areas are given with the Mathematica and other computer packages and computer languages. Basic computational tools and routines, including the ones for numerical integrations, differential equations, mathematical modeling, data visualization, spectral analysis, and matrix operations, are dealt with through relevant examples, and more advanced topics, such as quantum mechanics, mathematical methods in physics, geophysics, wavelet analysis, molecular dynamics, Monte Carlo simulations and quantum computing are also treated.

Course Content:
Introduction to computational Physics using Mathematica as the computational tool.

Uses of Mathematica  Animations
Mathematical Manipulations, Mathematica as a calculator, as Software package and as a Programming Language, Basic programming using Mathematica, Numerical Integration, Handling Functions, Simultaneous equations and Nonlinear equations, Data visualization using Plotting Functions, Conditionals and Loops, List and Table Manipulation for data sets and Matrices, Interpolation and Extrapolation, Complex Numbers, File Handling Input Box & Objects, Animations

Mathematical & Computational Modeling – A method used to forecast on time dependent variables using discrete data arrays. (Weather Forecasting, Stock Market, … etc)

Solving Differential Equations in Mathematical Physics, Maxwell’s Equations in Matter, 1D and 2D Wave Equations, Laplace Equation, Newton’s Law of motion and Molecular dynamics, Schrödinger equation, Electronic structure of atoms, …

Introducing Signal Processing Techniques
Simple Harmonic Motion and Damping Motion, Real Simple Physics Applications of Fourier Transforms (Forward and Inverse), Noise Elimination from Signals using FT, Fast Fourier Transform (FFT), Monte Carlo integration, Monte Carlo simulations, …
Introduce Wavelet analysis and solving simple applications in Physics using  Haa  Wavelet

Miscellaneous Problems:
LRC Network handling in AC Theory, solution of Schrödinger Equation in Quantum Mechanics, Problems of Gravity and Magnetism in Geophysics, 3D Gravity problem of rectangular shaped body (Forward & Inverse problems), Mathematical and Computational modeling in singhe variable parameter in Physics (Variation of the Average Temperature of Atmosphere with Time, Variation of Atmospheric CO2  percentage with Time, … etc)

 

Recommended Readings:

  1. A First Course in Computational Physics – Paul L. DeVries, John Wiley & Sons, Inc.
  2. Numerical Recipes : The Art of Scientific Computing – William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, Cambridge University Press.
  3. Numerical Methods for Physics – Alejandro L. Garcia
  4. Computer Simulation Methods, Applications to Physical Systems, Part 1 and Part 2 – Harvey Gould and Jan Tobochnik,
  5. The Mathematica Book, Fifth Edition, 2003 by Stephen Wolfram
  6. Programming with Mathematica, An Introduction. by Paul R. Wellin, 2013
  7. An Introduction to Modern Mathematical Computing with Mathematica. by Jonathan Borwein, Matthew P. Skerritt, 2012