Numerical Methods in Physics

Course content

The course is a hands-on introduction to the numerical and computational techniques used in modern physics. While most bachelor level physics courses present examples where there exist elegant analytical solutions, most real-world problems are solved with the help of computers and numerical techniques.

Focus will be on the application of numerical methods to example problems, but will also touch upon the theoretical foundations of many of these methods.

Education

BSc Programme in Physics

Learning outcome

Skills

After the course the students will be able to program numerical methods for solving numerous problems that arise in physics. These include:

  • Initial-value and boundary-value problems for Ordinary Differential Equations
  • Partial Differential Equations
  • Stochastic Simulations

Knowledge
The student will be able to recognise the different approaches that can be used to tackle a problem numerically and will understand the differences between using explicit vs. implicit time-stepping. The student will understand and be able to employ finite difference methods. The student will also be familiar with the existence of grid-free approaches such as spectral methods, and will be able to do simple stochastic simulations.

Competences
The student will gain some overview of numerical tools frequently used in modern physics. In addition, the student will be aware of potential caveats and will be able to better direct themselves in the extensive literature on numerical and computational techniques.

Lectures, exercises and project in groups.

Lecture notes will be available for the course. Further reading material will be posted on Absalon.

Basic programming (Python or any other programming language) and mathematical skills (linear algebra and differential equations).

It is expected that the student brings laptop with Python or similar programming environment installed. Examples will be given in Python. Observe that the course takes place over the 4 weeks and will thus require intensive participation.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
During the course students will have to hand in 3 written reports and do a group project followed up by presentation in class. The reports and the project must be approved to pass the course.
Aid
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
one internal examiner
Criteria for exam assessment

see 'skills'

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 15
  • Preparation
  • 40
  • Exercises
  • 95
  • Project work
  • 56
  • English
  • 206