1.1 How to study this course at 3 levels: the meaning of

Studying is fundamentally an individual process, where every student has to find out himself what is the most efficient method to understand and assimilate new concepts. Experience however shows that major steps are taken when a theory is first exposed by the teacher (in a regular classroom, a video-lecture or a syllabus), later reviewed and discussed with peers (best accross the table during coffee break, or if this is not possible, in a video-conference, during user forum discussions or even a computer quiz) and finally applied to solve practical problems.

The educational tools, which have been developed to study the course on-line reflect this pedagogical understanding. They can be combined in different manners, using technology to provide flexibility to study at the place, time, pace and level that best suits every learner. The progress made by every learner is continuously monitored with a system of bonus points: they reward original contributions from different activities, including user forum discussions and assignments that are performed with the help an corrections from a human teacher. Particularly nice solutions will be selected for reference and shared for discussions with the rest of the class.

An example showing how you can study the material during a typical day of an intensive course involves three distinct phases; those marked with an asterisk require that you login to enjoy full pedagogical support.

Passive learning (1h).

This is when new concepts are first brought to you and you only have to carefully follow the teacher's line of thought. In this phase, you may combine

• Video-Lecture. From the course main page, select COURSE: video-lecture and download the video file once for all to your local disk (press SHIFT + select link). This enables you to scroll back and forth, stop and replay different arguments in the lecture. If they are present, you can use the subtitles for synchronization with the syllabus on-line and perform the experiments directly as they are discussed in the video. Open your video player next to, or on the top of your web browser to work with both tools simultaneously-select Always on top when playing).
• Syllabus. Select the COURSE: printout to access the Java-powered document where you can execute all the virtual experiments on-line. You can also download and print the equivalent paper edition in PDF or Postsript format, using the browser only to perform the experiments and follow the links that appear in italic in the printed edition. Depending on your level and ambition, you can choose either to read or skip the material that is labelled on paper with symbols for intermediate and more advanced students. After login, the same material on-line will be displayed with grey fonts if a particular section is more advanced than the level that has been defined for you at the time of the registration.

Active learning (2h).

Following the passive phase, you are meant to question the validity of the new concepts, verify the calculations and test parametric dependencies.

• Syllabus. Repeat the analytical derivations that are on purpose left scarce to force you to fill-in the intermediate steps by yourself.
• Applets. Perform the numerical experiments that are suggested and modify the parameters to challenge your understanding. The original values can always be recovered with a partial reload of the webpage-simply by pressing the F5 key with Microsoft Explorer or selecting Reload with Netscape, Mozilla and Firefox.
• Quiz. Answer the review questions making sure that you properly understood all the material. Reading the syllabus on-line, you can verify your answer and follow a correction link directly back into the syllabus.
• Tutorials / Video-Conference. With a sufficient number of participants, tutorials (locally) or video-conferences (at a distance) are sometimes organized to discuss and refine the understanding that has PREVIOUSLY BEEN ACQUIRED in the passive phase. This is an opportunity for everyone not only to ask, but also to answer and comment the questions from peers.
• User Forum. Regular students choose the classroom (others the world ) forum both to obtain and provide help and also to improve the general understanding of the material. You are strongly encouraged to discuss related topics and share your views with answers to your classmates. Remember that this virtual classroom activity is mandatory and rewarded with 1-5 bonus points depending on the effort made for every contribution. Note that it does not really matter whether your arguments are correct or not: it is the teachers' duty to correct potential errors. Consult the Forum: rules and take a minute to think how you can make your contributions beneficial for everyone in the course (exercise 1.00).

Problem based learning (5h).

Having understood the principles, a new skill is finally acquired by solving practical problems. Select USER: login to open your personal account and list your problem set under WORK: assignments. Each exercise can be edited in your browser by clicking on the identification number (e.g. 1.00): below the handout, different windows invite you to edit (alt. cut-paste from an editor) and then submit your solution to different compilers:

• TeX. The first window can handle both regular text (ASCII) and L^ATEX input, allowing engineering students to enrich their solutions with mathematical derivations (symbols inserted between two dollar signs, such as $c=\sqrt{a^2+b^2}$, will appear as regular algebra in your web browser). In this TeX window, you should explain how you derive your solution, how you implement it and discuss the numerical values or plots you have observed in your experiments. In this TeX window, you should explain how you derive your solution, how you implement it and discuss numerical values or plots that you obtained in your experiments. Usually, the window opens with a template that contains a set of instructions and examples telling how you can format your solution: use them as you want, but please delete / replace this initial content with your own words before you submit a solution for correction to the teacher. The only exceptions are the lines tagged with a label of the form (VTQ1.00-1), where you give a specific answer that will be automatically checked by the course Virtual Teaching Assistant. Users who are not familiar with L^ATEX generally find it easy to start by performing only small modifications to the templates. A complete list of symbols symbols can be found in sect.9.1 and is most conveniently accessed using the link placed directly on the top of the TeX input window.
• JAVA. The content of the JAVA window will be inserted and compiled into an actual applet, allowing engineering students to develop and execute their own numerical schemes directly on-line. It is not necessary to know any Java programming to follow this course: most of the tasks involve small modifications of templates that are given and part of the syntax will automatically be acquired through the context. Be careful, however, to always correct all the compiler errors before you switch to another exercise... or the applet will stop working in all your assignments. For documentation concerning Java consult chapter 9.2, which can again be accessed directly from the top of the Java input window.

  Important for advanced students who will perform modifications to their Java code: most browsers store the applet once for all in a local cache directory. To a newly compiled version of your own applet, you have to force your browser to COMPLETELY reload the solution web page with all its components (check the frequently asked questions FAQ to find out how you can do this by clicking RIGHT in the white area and pressing CTRL-F5 with Microsoft Explorer, press SHIFT + select Reload using Netscape, or type 'x' in the Java console when using Mozilla and Firefox. Finally, if you don't get immediate programming advice from the User Forum, you may temporarily deactivate a problematic scheme using the /* Java comment delimiters */.

• Parameters. The tags window allows you to preset parameter values in your applet that are different in every exercise: choose them so as to highlight the phenomenon you want to illustrate. Only the parameters that appear in the tags will also be displayed in the applet.
• Figures. Screen copies produced with external software can be submitted as figures in bitmat format: png, gif, jpeg in decreasing order of preference.

Finally, be sure to submit only one input window at any time and always compile your work before you navigate further in the syllabus or in the forum. Sometimes the Back button of your browser may restore data that has been lost... but don't count on it! As soon as your solution is ready or when you need a specific piece of advice that only the teacher can provide, click on the CheckMe button (appearing on the left of every WORK: assignment after the first compilation) and press Submit Check (at the bottom of the table) to send your solution for correction to the teacher. Take into account the corrections that will be returned after a couple of days until the solution is accepted and your exercise is signalled as passed.

• Evaluation. The last section of every chapter consists of a short anonymous evaluation form where you are kindly requested to communicate your impressions each time before you start a new chapter. By sharing your impressions as you work yourself through the material, we will try to maximise your satifaction not only at the end of the course, but also optimize the path leading there.

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