DN2269 Mathematical Models, Analysis and Simulation, part 2 7.5 credits

Matematiska modeller, analys och simulering, del 2

A second course in numerical methods with a mathematical emphasis and a focus on real-world mathematical models.

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

Can vary from year to year.

In 03/04 the course treated stochastic differential equations and their numerical solution, with applications in financial mathematics, turbulent diffusion, control theory and Monte Carlo methods. We discussed basic questions for solving stochastic differential equations, e.g. to determine the price of an option is it more efficient to solve the deterministic Black and Scholes partial differential equation or use a Monte Carlo method based on stochastics.

The course treated basic theory of stochastic differential equations including weak and strong approximation, efficient numerical methods and error estimates, the relation between stochastic differential equations and partial differential equations, stochastic partial differential equations, variance reduction.

Intended learning outcomes *

The goal of the course is to

  • expose the students to and give them experience of important parts of applied and numerical mathematics,

so that they will be able to

  • analyze systems with infinite degrees of freedom both theoretically and computationally.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

One of the courses 2D1220/DN2220 Applied Numerical Methods I, 2D1225/DN2225 Numerical Solutions of Differential Equations, 2D1250/DN2250 Applied Numerical Methods II.. Some experience of computer programming and the use of UNIX systems or personal computers is also assumed. The course DN2269 Mathematical models, analysis and simulation, part II can be studied independently of course 2D1266/DN2266 Mathematical models, analysis and simulation, part I.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

To be announced at course start. Previous year material produced at the department was used.

Examination and completion

Grading scale *

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

Examination *

  • LAB1 - Laboratory Task, 3.7 credits, Grading scale: P, F
  • TEN1 - Examination, 3.8 credits, Grading scale: 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.

Other requirements for final grade *

Examination (TEN1; 3,8 university credits).
Assignments (LAB1; 3,7 university credits).

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Jesper Oppelstrup

Further information

Course web

No information inserted

Offered by

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

Please discuss with the instructor.

Contact

Lennart Edsberg, tel: 790 8119, e-post: edsberg@nada.kth.se

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.

Supplementary information

The course is not given 08/09.