PREFACE

This is the syllabus of the course taught at the Royal Institute of Technology in Stockholm (KTH course 2D5246, 4 points) to graduate students from engineering and quantitative social sciences. With the development of collaborative teaching and distance learning, the material is also shared with the Swedish Netuniversity (KTH course 2D4232, 4 points) the Swiss Federal Institute of Technology (EPFL, Lausanne) and Lifelong-Learners from the Internet.

Recognizing the value of an introductory level text describing a range of numerical methods for partial differential equations with practical examples, a problem based learning laboratory has been developed around a highly interactive document.Every problem is exposed all the way from the formulation of the master equation, its discretization resulting in a computational scheme, to the implementation with hyper-links directly into the JAVA source code. The JBONE applet executes every scheme with editable parameters and initial conditions that can be modified by the user. Comparisons of different methods show advantages and drawbacks that remain hidden when a method is exposed separately in a specialized book. The complete source code of the applet can be obtained free of charge for personal use after registration.

For this fifth web edition accessible to everyone on the Internet, I would like to thank Johan Carlsson, Johan Hedin, Thomas Johnson (KTH, Stockholm) and Laurent Villard (EPFL, Lausanne) who, since the first time this course was taught on-line in 1999, have all significantly contributed to enrich the course material. Ambrogio Fasoli (MIT, Cambridge) provided the measurement of an Alfvén instability to illustrate the importance of aliasing in the digital acquisition of data-an example from fusion energy research where we compare the solutions from numerical models with the world's largest tokamaks.

I hope that this learning environment will be useful to you. In any case, I will consider my task more than satisfactorily accomplished, if, by the end of the course, you will not be tempted to paraphrase Oscar Wilde's famous book review: ``Good in parts, and original in parts; unfortunately the good parts were not original, and the original parts were not good''.

André JAUN, Stockholm, August 2005

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