Taylor Series Expansion
2016+Week4
2016+Week4
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<strong>Taylor</strong> <strong>Series</strong> <strong>Expansion</strong><br />
Truncated <strong>Taylor</strong> <strong>Series</strong><br />
<strong>Expansion</strong><br />
y(<br />
x<br />
0<br />
<br />
h)<br />
<br />
n<br />
<br />
k<br />
h <br />
<br />
k!<br />
<br />
<br />
k<br />
d y<br />
dx<br />
k<br />
k 0 xx<br />
, y<br />
y<br />
0<br />
0<br />
<br />
<br />
<br />
<br />
<br />
y(<br />
x<br />
0<br />
)<br />
<br />
h<br />
dy<br />
dx<br />
xx<br />
y<br />
y<br />
0<br />
0<br />
,<br />
<br />
2<br />
h<br />
2!<br />
2<br />
d y<br />
2<br />
dx<br />
xx<br />
y<br />
y<br />
0<br />
0<br />
,<br />
...<br />
<br />
n<br />
h<br />
n!<br />
n<br />
d y<br />
n<br />
dx<br />
xx<br />
y<br />
y<br />
0<br />
0<br />
,<br />
The n th order <strong>Taylor</strong> series method uses the<br />
n th order Truncated <strong>Taylor</strong> series expansion.<br />
19
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