Example 12.  Given  [Graphics:Images/NumericalDiffMod_gr_283.gif], find numerical approximations to the derivative  [Graphics:Images/NumericalDiffMod_gr_284.gif], using three points and the forward difference formula.

Solution 12.

[Graphics:../Images/NumericalDiffMod_gr_285.gif]

[Graphics:../Images/NumericalDiffMod_gr_286.gif]

[Graphics:../Images/NumericalDiffMod_gr_287.gif]
[Graphics:../Images/NumericalDiffMod_gr_288.gif]

[Graphics:../Images/NumericalDiffMod_gr_289.gif]

[Graphics:../Images/NumericalDiffMod_gr_290.gif]
[Graphics:../Images/NumericalDiffMod_gr_291.gif]

[Graphics:../Images/NumericalDiffMod_gr_292.gif]

[Graphics:../Images/NumericalDiffMod_gr_293.gif]
[Graphics:../Images/NumericalDiffMod_gr_294.gif]

[Graphics:../Images/NumericalDiffMod_gr_295.gif]

[Graphics:../Images/NumericalDiffMod_gr_296.gif]
[Graphics:../Images/NumericalDiffMod_gr_297.gif]

[Graphics:../Images/NumericalDiffMod_gr_298.gif]

[Graphics:../Images/NumericalDiffMod_gr_299.gif]
[Graphics:../Images/NumericalDiffMod_gr_300.gif]

[Graphics:../Images/NumericalDiffMod_gr_301.gif]

[Graphics:../Images/NumericalDiffMod_gr_302.gif]
[Graphics:../Images/NumericalDiffMod_gr_303.gif]

Animation 2.  ( Numerical Differentiation  Numerical Differentiation ).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004