Short Course Description
Numerical Methods in Physics
Second year course
Prerequisites:
Basic knowledge in 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 describes the use of numerical and computational methods to solve physics problems that cannot be treated with conventional analytical approaches. We 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 mainly uses Python.
Possible topics include:
· 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), Monte-Carlo integration.
· Root finding (bracketing and bisection, Newton-Raphson).
· Minimum/Maximum problems (Simplex, Conjugate gradient).
· Fast Fourier transforms.
· Solving ordinary and partial differential equations (Euler and Runge Kutta methods).
· Fitting models to data (maximum likelihood).
Literature:
Numerical Recipes in C, by Press, Flannery, Teukolsky and Vetterling
Full Syllabus
