Calculus 6.1 day 2

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6.1 day 2
Eulers Method
First Peoples Buffalo Jump State Park, near Great
Falls, Montana
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6.1 day 2
Eulers Method
Pronounced oi-ler
Leonhard Euler was a Swiss mathematician who made
a huge number of contributions to mathematics,
almost half after he was totally blind.
(When this portrait was made he had already lost
most of the sight in his right eye.)
Leonhard Euler 1707 - 1783
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It was Euler who originated or popularized the
following notations
However, the symbol was not in common use until
1748 when Euler used it in Introductio in
Analysin Infinitorum.
Leonhard Euler 1707 - 1783
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There are many differential equations that can
not be solved. We can still find an approximate
solution.
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Exact Solution
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The TI-89 has Eulers Method built in.
Example
We will do the slopefield first
MODE
Graph..
6 DIFF EQUATIONS
We use y1 for y t for x
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6 DIFF EQUATIONS
Graph..
MODE
We use y1 for y t for x
not critical
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While the calculator is still displaying the
graph
yi110
tstep .2
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To plot another curve with a different initial
value
Either move the curser or enter the initial
conditions when prompted.
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The book refers to an Improved Eulers Method.
We will not be using it, and you do not need to
know it.
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