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Before choosing course

Course offering missing for current semester as well as for previous and coming semesters
* Retrieved from Course syllabus DN2280 (Autumn 2009–)

Content and learning outcomes

Course contents

Differential equations are fundamental for the modeling in Science and Engineering. As the computational power increase, it becomes feasible to use more accurate differential equation models and solve more demanding problems: for instance to determine input data from fundamental principles and to optimally reconstruct input data using measurements.The course includes lectures, computer exercises and student presentations on models, analysis and computational methods from nuclei-electron micro-systems to Euler and Navier-Stokes macro-systems for continuum fluids, using a unified mathematical method to derive and explain the coupling between the models on the different scales.
- Relation between Schrödinger-molecular dynamics-continuum partial differential equations

- Ehrenfest dynamics and surface-hopping

- the Born-Oppenheimer approximation

- electron structure calculation methods

- bridging ab initio and empirical molecular dynamics

- molecular dynamics: thermodynamics and statistical mechanics

- molecular dynamics: ensembles and simulations

- stochastic Langevin and Smolchuwski molecular dynamics

- molecular dynamics reaction paths and rates

- Euler and Navier-Stokes macroscopic equation derived from microscopic molecular dynamics

- project presentations on applications.

Intended learning outcomes

After completing this master level course the student will be able to model, analyze and compute solutions to multi-scale model problems from Schrödingers equation, for nuclei-electron systems, over molecular dynamics to Euler and Navier-Stokes equation for continuum fluids.

Course Disposition

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Literature and preparations

Specific prerequisites

Single course students: 90 university credits including 45 university credits in Mathematics or Information Technology. English B, or equivalent.

Recommended prerequisites

The prerequisite for the course is linear algebra, calculus, differential equations, probability and numerics corresponding to the first three years at KTH.


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Lecture notes.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • LAB1 - Laboratory, 3,5 hp, betygsskala: P, F
  • TEN1 - Examination, 4,0 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see:

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Profile picture Anders Szepessy

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web DN2280

Offered by


Main field of study

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Education cycle

Second cycle

Add-on studies

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Anders Szepessy, e-post:, tel: 790 6742

Supplementary information

The course is given as a reading course.