Course of Computational Physics I [SPHYM123]

Learning outcomes

The course aims at comforting the application of numerical techniques to problems that are typical of both experimental and theoretical physics. The different methods presented for these problems are demonstrated in class and used in computer-lab sessions.

Content

Table of contents

1. Working with gfortran
   Fortran 90 : advanced notions
   Representation of numerical data
2. Resolution of systems of linear equations
   Appendix : the LAPACK library
   Appendix : Octave (MATLAB)
3. Interpolation methods
   Linear interpolation, parabolic interpolation, polynom of Lagrange
   Interpolation by spline functions
   Interpolation in multiple dimensions
   Appendix : the Numerical Recipes
   Appendix : interpolation with Octave
4. Numerical Derivatives
   Asymmetric and symmetric formulas for a first derivative
   Romberg's algorithm
   Symmetric formula for a second derivative
   N-points formulas for arbitrary-order derivatives
5. Numerical Quadratures
   Trapezoidal rule, Simpson's rule
   Generalized Simpson formulas
   Adaptative Quadratures (quanc8)
   Gauss' method
   Appendix : integration with Octave
6. Linear adjustements
   Least squares method
   Generalized linear adjustments by a SVD decomposition
7. Optimization methods
   Minimization in one dimension (golden search)
   Minimization in several dimensions (gradient descend, conjugate gradient)
   Monte Carlo method (simulated annealing)
   Genetic Algorithms
   Appendix : optimization with Octave
8. Integration of differential equations
   Euler's method, multi-step method, predictor-corrector method, Runge-Kutta method
   Fourth-order Runge-Kutta method (rkf45)
   Appendix : integration of differential equations with Octave

Exercises description

Exercises consist in writting computer programs in Fortran 90 in order to solve typical problems in Physics.