Numerical Methods for Physics

Winter Semester 2024/2025 (lecture notes; exercises; codes)

Lectures:
Mon., 08:00-10:00, Room _0.111; Tue.,   08:00-10:00, Room _0.111
Changes to this schedule are announced in the Hochschulportal and will reported here as well (here the information about the tutoring and exercises).
 
Exercises:
Frid., 10:00-12:00, Room 02.120; Frid., 16:00-18:00, Room 02.120.
The tutors for the course are Claudio Meringolo and Jinliang Jiang. Two  groups will be organised distributing students in the different time slots.
Please register to the course by sending an email to Frau Steidl; this will help create a mailing list.
Information on the course

The course aims at providing the student with many of the “tools” frequently used in the solution of physical problems. The course is meant to be an applied course, in which the actual programming is a key feature. For this reason, each lecture will have one or more exercises involving the solution of a specific physical problem via the use of numerical codes implementing the techniques discussed in the lecture. The codes can be written in any of the following languages: fortran (77, 90, 95), C, C++, python. However no specific computational knowledge is necessary. Each exercise must be completed (ideally) before the subsequent lecture in the course starts. Topics covered include:

  • Root Finding
  • Linear Algebra
  • Interpolation and Extrapolation of functions
  • Integration of Functions
  • Random Numbers and Montercarlo Techniques
  • Solution of Ordinary Differential Equations
  • Solution of Partial Differential Equations:
    • Hyperbolic Equations
    • Parabolic Equations
    • Elliptic Equations
  • Fourier Transforms

Textbooks

  • Computational Physics, D. Potter, Wiley, NY
  • Numerical Methods for Conservation Laws, R. J. LeVeque, Birkhauser, 1992.
  • Numerical Recipes, W. H. Press et al., Cambridge Univ. Press, 1992
  • Relativistic Hydrodynamics, L. Rezzolla and O. Zanotti, Oxford Univ. Press, 2013