Computational Physics 1 (Fundamental Numerical Methods)

Module PH2057

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2057 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 75 h 5 CP

Responsible coordinator of the module PH2057 is Stefan Recksiegel.

Content, Learning Outcome and Preconditions


1. Introduction
‒ Numbers on computers
‒ Sources of errors
2. Integration
‒ Riemann definition
‒ Trapezoid rule, Simpson rule
‒ Gauss integration
‒ Adaptive stepsize
3. Differentiation
‒ Forward Difference, Central Difference
‒ Higher Orders
4. Root Finding
‒ Bisection
‒ Newton-Raphson
5. Linear Algebra
‒ Gauss elimination with back-substitution
‒ LU-Decomposition
‒ Singular Value Decomposition
6. Multidimensional Newton-Raphson
7. Data fitting / Inter-/Extrapolation
‒ Lagrange interpolation, Splines
‒ Least squares fit
‒ Linear least squares, non-linear chi^2
8. Ordinary Differendial Equations
‒ Classification of DEs
‒ Euler algorithm
‒ Midpoint algorithm
‒ Runge-Kutta
‒ Applications: Planetary motion, etc.
‒ Initial/boundary value problems
‒ ODE eigenvalues
9. Partial Differential Equations
‒ Elliptic PDEs
‒ Parabolic PDEs
‒ Hyperbolic PDEs

Learning Outcome

At the end of the module CPI students are able to understand and implement (in various programming languages) basic numerical methods such as integration, (multidimensional) root finding, data interpolation and fitting. They are able to classify and numerically solve all ordinary and simple partial differential equations and to construct a proper DE description for a given physical problem.


No preconditions in addition to the requirements for the Master’s program in Physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 4 Computational physics 1 Recksiegel, S. Dienstag, 14:00–16:00
sowie Termine in Gruppen

Learning and Teaching Methods

lecture, video projector presentation, board work, exercises in individual and group work


practise sheets, accompanying web page:


Much of the material in this course is covered in "“Computational Physics: Problem Solving with Computers”" by Landau, Paez and Bordeianu, Wiley-Vch, ISBN 3527406263.

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester. There is a possibility to take the exam in the following semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Prüfung zu Rechnergestützte Physik 1
Di, 11.4.2017, 11:00 bis 12:30 Physik I: 2502
bis 3.4.2017 (Abmeldung bis 4.4.2017)
Di, 14.2.2017, 13:30 bis 15:00 Physik I: 2501
bis 15.1.2017 (Abmeldung bis 7.2.2017)

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.