Example 10.  Given  [Graphics:Images/NumericalDiffMod_gr_241.gif], find numerical approximations to the derivative  [Graphics:Images/NumericalDiffMod_gr_242.gif], using two points and the backward difference formula.

Solution 10.

[Graphics:../Images/NumericalDiffMod_gr_243.gif]

[Graphics:../Images/NumericalDiffMod_gr_244.gif]

[Graphics:../Images/NumericalDiffMod_gr_245.gif]
[Graphics:../Images/NumericalDiffMod_gr_246.gif]

[Graphics:../Images/NumericalDiffMod_gr_247.gif]

[Graphics:../Images/NumericalDiffMod_gr_248.gif]
[Graphics:../Images/NumericalDiffMod_gr_249.gif]

[Graphics:../Images/NumericalDiffMod_gr_250.gif]

[Graphics:../Images/NumericalDiffMod_gr_251.gif]
[Graphics:../Images/NumericalDiffMod_gr_252.gif]

[Graphics:../Images/NumericalDiffMod_gr_253.gif]

[Graphics:../Images/NumericalDiffMod_gr_254.gif]
[Graphics:../Images/NumericalDiffMod_gr_255.gif]

[Graphics:../Images/NumericalDiffMod_gr_256.gif]

[Graphics:../Images/NumericalDiffMod_gr_257.gif]
[Graphics:../Images/NumericalDiffMod_gr_258.gif]

[Graphics:../Images/NumericalDiffMod_gr_259.gif]

[Graphics:../Images/NumericalDiffMod_gr_260.gif]
[Graphics:../Images/NumericalDiffMod_gr_261.gif]

Animation 3.  ( Numerical Differentiation  Numerical Differentiation ).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004