1. Mat-F February 23, 2005 Separation of variables Åke Nordlund Niels Obers, Sigfus Johnsen / Anders Svensson Kristoffer Hauskov Andersen Peter Browne Rønne

2. Overview Follow-up Computer procedures to avoid troubles to solve a problem one must understand it New web pages useful links! Chapter 19 Separation of variables with Maple Exercises today Examples (that one can hack) are very useful!

3. Follow-up: Computer problems Client-server setup Over-loaded servers – not really! Over-loaded network?? No! Server problems at fys.ku.dk last week Browser problems Mozilla / Netscape + JAVA with Maple TA does not work! Use galeon (unlikely but works!) Don’t panic! “… it said in warm, red letters …”

4. Optimizing computer performance load average page (teachers in RF) for choice of unused hosts Do not use KDE! use Gnome or Debian Do not use Mozilla / Netscape use galeon

5. Monitoring today I will be monitoring behind the scene Network load Computer loads Please report any strange behavior! To me if I’m in the room To the exercise teacher if I’m not!

6. General Feedback Report back about anything which is unclear! Talk to the exercise teacher better ‘bandwidth’ than ‘web discussion group’ don’t be afraid to ask; no question is too silly! immediate answers in many cases We will collect notes in a teacher ‘blog Feedback based on this web material updates feedback during lectures and exercises

7. New web material PowerPoint lecture material Available directly from the ‘schedule’ page Links Dictionaries Math and phys knowledge bases Maple procedures

8. Examples of useful link info Dictionaries, for unfamiliar words Merriam-Webster Wordnet Engelsk-dansk … What is sinh(x) and cosh(x)? www.ask.com  plots and explanations www.ask.com World of Math  background ‘cosh is the shape of a hanging cable’ read about the background for the names

9. Preparations for next week Check the Schedule page! Read / browse 19.3 – 19.5 Don’t panic! Look at some of the exercises Monday will be based on 19.5 and 19.10-12 Don’t panic!

10. Todays exercise Using Maple to explore solutions Combining analysis and visualization You get a heat diffusion Maple worksheet rectangular sheet solutions constructed and animated You should make a wave equation ditto rectangular membrane construct membrane wave solutions animate them!

11. PDEs: What Maple can and cannot do It can solve some PDEs numerically with two variables: directly (dsolve/numeric) with more variables: indirectly – see web repository! give analytical solutions to many relevant PDEs visualize and animate these It cannot Handle boundary conditions well analytically Solve for example 2-D plus time PDEs numerically such as the ones for today

12. Enough for today! Good luck with the Exercises!