Nada

2D4232, Numerical Methods for Partial Differential Equations (distance-learning, 4 points / 6 ECTS)

Numerical methods are a part of the problem solving skills that are expected to be mastered by most of the university graduates working in a quantitative field. The same fundamental concepts of Brownian motion, convection, diffusion, dispersion and non-linearity are used to simulate applications in telecommunication (collisions of data-packets in a network, solitons in optical fibers), economics (stock options), biology (transport in cellular tissues), engineering (heat transfer, pollution) and social sciences (behavior of people in a crowd). Quantitative answers for real applications can generally be obtained only from computations.

What are the course targets?

The target of this course is to provide a working knowledge in at least four numerical methods and to apply them for a variety of equations.

Content

The Java powered syllabus introduces finite differences, finite elements, fast Fourier transforms, Monte-Carlo and Lagrangian schemes. Each method is illustrated and applied with experiments to solve practical problems in one dimension, including the advection-diffusion (heat transfer), Black-Scholes (option pricing), Burger (shock waves), Korteweg-De Vries (solitons) and the Schrödinger equation (quantum mechanics).

Distance-learning and assessement

The course can be completed at a distance using a regular browser to submit assignments with derivations and programs in a problem based learning environment. A strong emphasis is put on the problem based learning where the participants analyze data, derive, implement, document and execute their own models in a web browser everywhere on the Internet. The first part of the course consists in a number of self-studies and assignments with computer generated feed-back that can be completed throughout the year (2 points / 3 ECTS). The second part involves more complex problem based learning tasks that are completed under the supervision of a human teacher when the course officially takes place (2 points / 3 ECTS) and has to be completed to finally qualify for a course certificate.

Target group

Advanced undergraduates / PhD students with a scientific background.

Prerequisites

Ordinary differential equations, Fourier analysis and elementary programming.

Course website, contact and registration

More information and examples can directly be accessed from the course website (http://www.lifelong-learners.com/pde/nu/). To register, internal students can simply open an account during the month before the course starts. Netuniversity and continued education students from outside KTH have to fill-in the application form (select "Blankett") before the course starts. Specific questions preferably by e-mail to André Jaun, NADA, KTH, 100 44 Stockholm, tel +4670 7971879.

Course analysis

Here is a link to the analysis for the previous courses: 2005

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Content: André Jaun <remooove-this-field.jaun@nada.kth.se>
Last modified 16 Dec 2005
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