06.12.2016 Views

Taylor Series Expansion

2016+Week4

2016+Week4

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Finite Differences for Derivation<br />

.....<br />

)<br />

'''(<br />

3!<br />

)<br />

''(<br />

2!<br />

)<br />

'(<br />

)<br />

(<br />

)<br />

(<br />

3<br />

2<br />

<br />

<br />

<br />

<br />

<br />

<br />

x<br />

F<br />

h<br />

x<br />

F<br />

h<br />

x<br />

hF<br />

x<br />

F<br />

h<br />

x<br />

F<br />

.....<br />

)<br />

'''(<br />

3!<br />

2<br />

)<br />

'(<br />

2<br />

)<br />

(<br />

)<br />

(<br />

3<br />

<br />

<br />

<br />

<br />

<br />

<br />

x<br />

F<br />

h<br />

x<br />

hF<br />

h<br />

x<br />

F<br />

h<br />

x<br />

F<br />

)<br />

(<br />

)<br />

(<br />

'<br />

2<br />

)<br />

(<br />

)<br />

( 3<br />

h<br />

O<br />

x<br />

F<br />

h<br />

h<br />

x<br />

F<br />

h<br />

x<br />

F<br />

<br />

<br />

<br />

<br />

<br />

Central Difference Formula<br />

h<br />

h<br />

x<br />

F<br />

h<br />

x<br />

F<br />

x<br />

F<br />

2<br />

)<br />

(<br />

)<br />

(<br />

)<br />

'(<br />

<br />

<br />

<br />

<br />

.....<br />

)<br />

'''(<br />

3!<br />

)<br />

''(<br />

2!<br />

)<br />

'(<br />

)<br />

(<br />

)<br />

(<br />

3<br />

2<br />

<br />

<br />

<br />

<br />

<br />

<br />

x<br />

F<br />

h<br />

x<br />

F<br />

h<br />

x<br />

hF<br />

x<br />

F<br />

h<br />

x<br />

F

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!