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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.

Module version of WS 2010/1

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2020/1WS 2019/20WS 2018/9WS 2017/8WS 2010/1

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.

  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Complementary catalogue of special courses for Biophysics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

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 in the version of WS 2010/1 was 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

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

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be: Use the trapezoidal rule to calculate the integral of a function and show that the result is exact for linear functions.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

Exam Repetition

The exam may be repeated at the end of the 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.

Exam on Computational Physics 1
Tue, 2024-02-20, 11:00 till 12:30 Hörsaal
till 2024-01-15 (cancelation of registration till 2024-02-13)
Tue, 2024-03-26, 13:30 till 15:00 102
till 2024-03-21
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