Numerical Methods in Physics
Second year course

Prerequisites:
Basic knowledge in C programming (at the level of the Computers for Physicists course or equivalent), Math. Introduction for Physicists 1, Methods of Theoretical Physics 1 (studied in parallel).

Description:
This course will describe the use of numerical and computational methods to solve physics problems which cannot be treated by conventional analytical approaches. We will show how these numerical techniques can be translated to a computer program using either standard libraries or by developing the code ourselves. The goal is to expose the students to a variety of tools. The course uses mainly the C programming language, including the use of Numerical Recipes routines. Students will also learn how to use Matlab and Mathematica.
 

Topics:
 

·        Roundoff error and stability.
·        Solution of linear algebraic equations ( Gauss-Jordan elimination, LU decomposition, Singular Value decomposition).
·        Interpolation and extrapolation (polynomial method, Cubic spline).
·        Integration of functions ( Trapezoidal method, Simpson's method, Romberg integration).
·        Random numbers (uniform deviates, transformation methods).
·        Root finding (bracketing and bisection, Newton-Raphson).
·        Minimum/Maximum problems (Simplex, Conjugate gradient).
·        Fast Fourier transforms.
·        Partial differential equations (Euler and Runge Kutta methods).
·        Fitting models to data (maximum likelihood).
 

Literature:

a.        Numerical Recipes in C, by Press, Flannery, Teukolsky and Vetterling
b.       http://www.nr.com