Example 14.  Given  [Graphics:Images/NumericalDiffMod_gr_325.gif], find numerical approximations to the derivative  [Graphics:Images/NumericalDiffMod_gr_326.gif], using three points and the central difference formula.

Solution 14.

[Graphics:../Images/NumericalDiffMod_gr_327.gif]

[Graphics:../Images/NumericalDiffMod_gr_328.gif]

[Graphics:../Images/NumericalDiffMod_gr_329.gif]
[Graphics:../Images/NumericalDiffMod_gr_330.gif]

[Graphics:../Images/NumericalDiffMod_gr_331.gif]

[Graphics:../Images/NumericalDiffMod_gr_332.gif]
[Graphics:../Images/NumericalDiffMod_gr_333.gif]

[Graphics:../Images/NumericalDiffMod_gr_334.gif]

[Graphics:../Images/NumericalDiffMod_gr_335.gif]
[Graphics:../Images/NumericalDiffMod_gr_336.gif]

[Graphics:../Images/NumericalDiffMod_gr_337.gif]

[Graphics:../Images/NumericalDiffMod_gr_338.gif]
[Graphics:../Images/NumericalDiffMod_gr_339.gif]

[Graphics:../Images/NumericalDiffMod_gr_340.gif]

[Graphics:../Images/NumericalDiffMod_gr_341.gif]
[Graphics:../Images/NumericalDiffMod_gr_342.gif]

[Graphics:../Images/NumericalDiffMod_gr_343.gif]

[Graphics:../Images/NumericalDiffMod_gr_344.gif]
[Graphics:../Images/NumericalDiffMod_gr_345.gif]

Animation 5.  ( Numerical Differentiation  Numerical Differentiation ).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004