Transcript Mat-F, spring 2005 Partial Differential Equations

Mat-F
February 23, 2005
Separation of variables
Åke Nordlund
Niels Obers, Sigfus Johnsen / Anders Svensson
Kristoffer Hauskov Andersen
Peter Browne Rønne
Overview
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Follow-up
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Computer procedures to avoid troubles
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New web pages
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to solve a problem one must understand it
useful links!
Chapter 19
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Separation of variables with Maple
Exercises today
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Examples (that one can hack) are very useful!
Follow-up:
Computer problems
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Client-server setup
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Browser problems
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Over-loaded servers – not really!
Over-loaded network?? No!
Server problems at fys.ku.dk last week
Mozilla / Netscape + JAVA with Maple TA does not work!
Use galeon (unlikely but works!)
Don’t panic!
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“… it said in warm, red letters …”
Optimizing computer
performance
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load average page (teachers in RF)
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Do not use KDE!
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for choice of unused hosts
use Gnome or Debian
Do not use Mozilla / Netscape
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use galeon
Monitoring today
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I will be monitoring behind the scene
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Network load
Computer loads
Please report any strange behavior!
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To me if I’m in the room
To the exercise teacher if I’m not!
General Feedback
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Report back about anything which is unclear!
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Talk to the exercise teacher
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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
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web material updates
feedback during lectures and exercises
New web material
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PowerPoint lecture material
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Available directly from the ‘schedule’ page
Links
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Dictionaries
Math and phys knowledge bases
Maple procedures
Examples of useful link info
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Dictionaries, for unfamiliar words
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Merriam-Webster
Wordnet
Engelsk-dansk
…
What is sinh(x) and cosh(x)?
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www.ask.com  plots and explanations
World of Math  background
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‘cosh is the shape of a hanging cable’
read about the background for the names
Preparations for next week
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Check the Schedule page!
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Read / browse 19.3 – 19.5
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Don’t panic!
Look at some of the exercises
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Monday will be based on 19.5 and 19.10-12
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Don’t panic!
Todays exercise
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Using Maple to explore solutions
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Combining analysis and visualization
You get a heat diffusion Maple worksheet
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rectangular sheet
solutions constructed and animated
You should make a wave equation ditto
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rectangular membrane
construct membrane wave solutions
animate them!
PDEs:
What Maple can and cannot do
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It can
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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
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Handle boundary conditions well analytically
Solve for example 2-D plus time PDEs numerically
 such as the ones for today
Enough for today!
Good luck with the Exercises!