Example 13.  Given  [Graphics:Images/NumericalDiffMod_gr_304.gif], find numerical approximations to the derivative  [Graphics:Images/NumericalDiffMod_gr_305.gif], using three points and the backward difference formula.

Solution 13.

[Graphics:../Images/NumericalDiffMod_gr_306.gif]


[Graphics:../Images/NumericalDiffMod_gr_307.gif]

[Graphics:../Images/NumericalDiffMod_gr_308.gif]
[Graphics:../Images/NumericalDiffMod_gr_309.gif]

[Graphics:../Images/NumericalDiffMod_gr_310.gif]

[Graphics:../Images/NumericalDiffMod_gr_311.gif]
[Graphics:../Images/NumericalDiffMod_gr_312.gif]

[Graphics:../Images/NumericalDiffMod_gr_313.gif]

[Graphics:../Images/NumericalDiffMod_gr_314.gif]
[Graphics:../Images/NumericalDiffMod_gr_315.gif]

[Graphics:../Images/NumericalDiffMod_gr_316.gif]

[Graphics:../Images/NumericalDiffMod_gr_317.gif]
[Graphics:../Images/NumericalDiffMod_gr_318.gif]

[Graphics:../Images/NumericalDiffMod_gr_319.gif]

[Graphics:../Images/NumericalDiffMod_gr_320.gif]
[Graphics:../Images/NumericalDiffMod_gr_321.gif]

[Graphics:../Images/NumericalDiffMod_gr_322.gif]

[Graphics:../Images/NumericalDiffMod_gr_323.gif]
[Graphics:../Images/NumericalDiffMod_gr_324.gif]

Animation 4.  ( Numerical Differentiation  Numerical Differentiation ).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004