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Topic: Slopefields and Euler's Method
Replies: 5   Last Post: Jan 13, 1998 3:45 PM

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himtn@ecpi.com

Posts: 156
Registered: 12/6/04
Slopefields and Euler's Method
Posted: Oct 13, 1997 9:08 PM
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I teach AP Calculus, both AB and BC, and as many of you (I think ???) I am
trying to determine the most effective way of introducing Euler' Method and
slopefields. I took Diff Eq in the 70's, but I don't recall a lot of
attention given to slopefields ... or Euler's method for that matter.

I would appreciate any comments, corrections, suggestions, etc. that you may
care to make.

It seems to me that a slopefield is a diagram of many local linear
approximations of the solutions of a given DE through selected points
representing associated boundary values. Euler's method seems to take one
particular boundary value and construct an approximation to that particular
solution ... which also uses local linear approximations to determine
successive data points for the approximate solution. This method seems to
improve its accuracy as the increment of evaluation decreases.

Is this right?

TIA

Michael Mullen
Westwood High School
Austin, TX





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