MM837: Computational Physics
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310007102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310007101
ECTS value: 10
Date of Approval: 25-04-2019
Duration: 1 semester
Version: Approved - active
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to have knowledge of:
- Differentiation and integration of functions of one and several variables
- Basic concepts of linear algebra (vector spaces, matrices, eigenvalues ...)
- Ordinary Differential Equations
- Basic programming.
Course introduction
The aim of the course is to enable the student to apply computational
methods in order to solve non-trivial problems in nonetheless practical
and efficient way. Computational methods have become a standard approach
in many areas of science, especially in condensed matter, particle
physics, hydrodynamics, plasma-dynamics, biophysics and chemistry.
The course provides tools to address problems which typically cannot be
solved by analytical methods.
methods in order to solve non-trivial problems in nonetheless practical
and efficient way. Computational methods have become a standard approach
in many areas of science, especially in condensed matter, particle
physics, hydrodynamics, plasma-dynamics, biophysics and chemistry.
The course provides tools to address problems which typically cannot be
solved by analytical methods.
The course builds on the knowledge acquired in the courses DM550 (Introduction
to Programming) , MM547 (Ordinary Differential Equations: Theory,
Modelling and Simulation ), MM536 (Calculus for Mathematics) and MM538
(Algebra and Linear Algebra) .
The course is of high
multidisciplinary value and gives an academic basis for a Master thesis
project in several core areas of Natural Sciences.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to :
- handle complex and development-oriented situations in study and work contexts.
- to
independently engage in disciplinary and interdisciplinary
collaboration with a professional approach based on group -based
project. - Give skills to:
- analyze practical and theoretical problems with the help of numerical simulation based on a suitable mathematical model.
- analyze a mathematical model qualitative and quantitative traits.
- describe and evaluate sources of error for the modeling and calculation for a given problem.
- Give knowledge and understanding of:
- mathematical modeling and numerical analysis of problems in science and technology.
- how scientific knowledge is achieved by an interplay between theory, modeling and simulation.
Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:
- Reflect
on the numerical and algorithmic principles presented during the course
and connect them with other numerical/computational techniques from
other courses in the curriculum. - Reflect on the most appropriate solution techniques for the problem at hand, based on the knowledge acquired in the curriculum.
- Present and reflect on the scientific results achieved in a scientifically correct way.
Content
The following main topics are contained in the course:
- Numerical methods for classical Hamiltonian systems
- The N-body problem
- Integration schemes
- Numerical methods for Schroedinger equation in one dimension
- Monte Carlo Simulations of Spin Systems:
- Markov chains and Metropolis algorithm
- Cluster algorithm
- Wang-Landau algorithm
- Simulation of two-dimensional models
- Numerical Simulation in Quantum Field Theories
- Heatbath algorithm for Yang-Mills theories
- Hybrid Monte Carlo algorithm for matter fields
Literature
Examination regulations
Exam element a)
Timing
Autumn
Tests
Mandatory assignments
EKA
N310007102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
10
Indicative number of lessons
Teaching Method
In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 84 lectures, class lessons, etc. on a semester. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
- Intro phase (lectures, class lessons) - 56 hours
- Training phase: 28 hours
Activities during the study phase:
- preparation of exercises in study groups
- preparation of projects
Teacher responsible
| Name | Department | |
|---|---|---|
| Benjamin Jäger | jaeger@imada.sdu.dk | Computational Science |
| Michele Della Morte | dellamor@cp3.sdu.dk | Computational Science |