1
Euler's Method
Section 2.7
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2
Recall
•
As long as the coefficients of our 1
st
order
differential equation are continuous with
continuous partial derivatives with respect to y, it
has a unique solution surrounding the initial
point.
•
It is usually not possible to find the solution by
symbolic manipulations such as elementary
integration.
So far we have just studied the
exceptions to the rule. Namely, those equations
that are linear, separable, exact, or those that can
be transformed into one of these types.
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3
What do we do with the
problem children?
Since the vast majority of 1
st
order
differential equations cannot be solved using
the methods we have learned so far, we have
to have some way of dealing with them. On
the next two slides you will see our choices.
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4
Choice 1:
Direction Fields
We could have a computer algebra system
draw a direction field for us, which we could
use to visualize the behavior of solutions.
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 Fall '10
 PamelaSatterfield
 Derivative

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