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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 2018/9

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.

150 h 60 h 5 CP

Responsible coordinator of the module PH2057 in the version of WS 2018/9 was Stefan Recksiegel.

### Content, Learning Outcome and Preconditions

#### Content

1. Introduction
‒ Numbers on computers
‒ Sources of errors
2. Integration
‒ Riemann definition
‒ Trapezoid rule, Simpson rule
‒ Gauss integration
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

After successful completion of this module, students are able to

• understand and implement (in various programming languages) basic numerical methods such as integration, (multidimensional) root finding, data interpolation and fitting.
• classify and numerically solve all ordinary and simple partial differential equations.
• construct a proper DE description for a given physical problem.

#### Preconditions

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

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 2 Computational physics 1 Recksiegel, S. Tue, 14:00–16:00, PH HS2
Tue, 14:00–16:00, virtuell
eLearning
documents
virt.  lecturehall
VO 2 Introduction to Programming Recksiegel, S. Thu, 15:30–17:30, PH 1161
UE 2 Exercise to Computational Physics 1 Recksiegel, S. dates in groups documents
virt.  lecturehall

#### Learning and Teaching Methods

This module consists of a lecture and an exercise class.

In the lecture, the contents are first explained on a theoretical level on an electronic whiteboard (the slides can be downloaded from the lecturer's web site immediately after the lectures). Then, the algorithms are implemented in the computer algebra system Mathematica to study the practical applicability of the concept. Whenever possible, the students are asked for input during this process, and if a suggested approach fails (e.g. due to numerical instabilities), the causes are discussed and alternatives are presented.

Exercise sheets (which frequently include reproduction of the results of the lecture) are first worked on individually by the students and then discussed in small groups (exercises) under supervision.

Students are invited to a guided tour to the Leibniz Supercomputing Centre (LRZ). Additionally an introduction to programming is offered. This lecture is directed especially and especially recommended to students without programming experience.

#### Media

Presentations on an electronic Whiteboard, demonstrations in Mathematica, C and Python ; exercise sheets. Accompanying web page: http://users.ph.tum.de/srecksie/lehre

#### Literature

• R.H. Landau, M.J. Páez and C.C. Bordeianu: Computational Physics: Problem Solving with Computers, Wiley-Vch, (2007)
• G.P. Lepage: Lattice QCD for Novices, arXiv, (2005), http://arxiv.org/abs/hep-lat/0506036

### 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.
• What is the order of magnitude of the error for non-linear functions (in terms of the step size and derivatives of the function to be integrated)?
• Taking into account the algorithmic error and the roundoff error, what is the optimum number of integration steps?

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.

Title
TimeLocationInfoRegistration
Exam on Computational Physics 1
Wed, 2021-02-24, 11:30 till 13:00 Bitte lesen Sie vor der Anmeldung die Hinweise unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/ - insbesondere, wann Sie nicht zur Prüfung erscheinen dürfen und, was Sie beachten sollten, wenn Sie einer Risikogruppe für einen schweren Verlauf einer COVID-19-Erkrankung angehören. // Please read the information at https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/ carefully - especially the conditions in which you must not come to the exam and the necessary measures if you belong to a risk group for a severe progression of a COVID-19 case. till 2021-01-15 (cancelation of registration till 2021-02-24)
Wed, 2021-03-24, 11:00 till 12:30 Bitte lesen Sie vor der Anmeldung die Hinweise unter https://www.tum.de/die-tum/aktuelles/coronavirus/corona-lehre-pruefungen/ - insbesondere, wann Sie nicht zur Prüfung erscheinen dürfen und, was Sie beachten sollten, wenn Sie einer Risikogruppe für einen schweren Verlauf einer COVID-19-Erkrankung angehören. // Please read the information at https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/ carefully - especially the conditions in which you must not come to the exam and the necessary measures if you belong to a risk group for a severe progression of a COVID-19 case. till 2021-03-22 (cancelation of registration till 2021-03-24)
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