Who is this course for?
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 goal is to cover a wide range of numerical methods with simple examples to analyze building blocs that are used in complex simulation codes. A broad knowledge is often decisive to choose the right method when developing a new code. 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 course covers finite-differences, finite-elements, Fourier and Monte-Carlo methods and Lagrangian schemes; in each case, the algorithm is illustrated with prototype problems including the Fokker-Plank (transport), Black-Scholes (stock options), Burger (shock waves), Korteweg-DeVries (solitons) and Schrödinger equations.
Students who fulfill the course requirements obtain 4 Ladok / 6 ECTS credit points in the Swedish academic system or a course certificate showing that they met all the requirements to pass the postgraduate course for an equivalent of 4 weeks full time work -- an accreditation to reward professionals even within their own company.

Prerequisites.
To benefit from most of the material, participants need to have a basic knowledge in differential calculus, complex analysis and need to have a rough idea of what is a Fourier transformation. Few of these analytical techniques will be used, since most are carried out with the computer; the underlying concepts, however, remain the same and will not be exposed. Elementary programming is sufficient to modify templates and pick-up the knowledge in LaTeX, Java and HTML used to hand-back the assignments at a distance.

Flexible self-learning environment.
Apart from a tutorial that may be organized locally at the begining of a the Netuniversity course, all the material and the human support is accessible anytime from anywhere via the Internet. Each module corresponding to a chapter in the syllabus has its own set of assignments: they are carried out when time allows and are submitted for correction to a human teacher directly from a web browser. Help is provided by teachers and other participants in the classroom forum; this is where students meet informally and create professional contacts. The problem based self-learning environment used in this course is particularly well suited for a lifelong learning students who have professional obligations and cannot attend classes on a regular basis.

Admission, tuition fee, sponsorship.
Graduate students affiliated with a public university in Europe can participate free of charge in the Netuniversity course sponsored by the Swedish government (see below). Self-learners from sister universities and developing countries (who cannot easily afford to pay the price of a book) are sponsored by Lifelong-learners: they are warmly encouraged to register free of charge. Other learners who want to study outside the Netuniversity course period have to pay a fee for their teaching support.

Distance learning schemes

Our cyber tutoring remains accessible throughout the year; continued education with human support outside the academic framework is however not formally offered nor supported by the Royal Institute of Technology. A paying service is maintained by the teachers and can be accessed from this website. To open an account and start studying, all you need is to complete the registration form with a valid e-mail address where we can send your password and maintain a regular contact with you. A variety of learning schemes are designed to provide different levels of support and depend whether you are affiliated with a university or not.

0. Free-learning (for universities & developing world)
Self-learners from sister universities and the developing world (who cannot easily afford to pay the fee of a book) have been sponsored by Lifelong-learners since 1999 and are warmly welcome to register free of charge; others are kindly requested to register for a paying scheme.

1. Self-learning / download (US$ 48)
Independent learners may choose to study without the advice and corrections from a human Teacher and yet benefit from the distance-learning environment: unrestricted access to the Java powered and printout versions of the syllabus, RealVideo recordings and a problem solving environment to perform and store practical assignments. Help and advice is exchanged on a voluntary basis by the participants in a public discussion forum. A small license fee is collected to support the development of the material; in recognition for your payment, you will be given full access to the JBONE-4.0 source code for your own personal use. There is however no accreditation delivered for this form of self-learning.

2. Virtual classroom (US$ 980, certificate)
In addition to the self-learning environment, this scheme allows you to join a virtual classroom moderated by teachers on whom you can rely for advice and corrections within 2-3 working days. This working scheme qualifies for a course certificate provided that all the requirements are met. The tuition fee for this learning scheme covers the human support from the teachers; please contact André Jaun (tel: +46 70 7971879) to enquire about their availability.

3. Virtual tutor (US$ 2980, certificate)
These are really private lessons over the Internet; they are organized for one student by the course leader and rely on a working schedule that has been agreed upon. The tuition fee for this learning scheme covers the dedicated work from one teacher; please contact André Jaun (tel: +46 70 7971879) for more information concerning private lessons tailored to your request(s).

Special courses planned during the year 2006

These courses are organized in collaboration with top level universities or companies and are limited in time.

Swedish Netuniversity (2 October - 15 December 2006, 4pts, 6ECTS)
This is the regular course taught at the Royal Institute of Technology (KTH) internally to graduate students (2D5246), externally to continued education students (2D4232) and is free of charge for students who are affiliated with a public university in Europe. Apart from an optional tutorial that is given at KTH in Stockholm, the course can be completed entirely at a distance within the Swedish Netuniversity context. To register, qualifying participants have both to fill-in an application form (preferably before 15 May) and to open an account on the dedicated website -- Swedish residents please provide your complete 10 digits personal number, others your date of birth in the form YYMMDD.

Doctoral school, Ecole Polytechnique Fédérale de Lausanne (6ECTS)
A doctoral course has been organized in 2001, 2003 and 2005 in a partnership between Laurent Villard (EPFL) and André Jaun (KTH) and will presumably be taught again during 2007. Students contact their local respondant for an up-to-date information and complete their registration on-line without forgetting to specify their complete date of birth (dd-mm-yyyy) to allow for the transfer of academic credits.

Private companies and firms
The list can not be disclosed here; specific information will be displayed on your Intranet if a course is organized. If you would like to organize such a course, please contact André Jaun (tel: +46 70 7971879) to enquire about the possibilities.