Explore Numerical Computations
![[Graphics:../Images/CauchyRiemannMod_gr_52.gif]](../Images/CauchyRiemannMod_gr_52.gif)
![[Graphics:../Images/CauchyRiemannMod_gr_54.gif]](../Images/CauchyRiemannMod_gr_54.gif)
![[Graphics:../Images/CauchyRiemannMod_gr_56.gif]](../Images/CauchyRiemannMod_gr_56.gif)
We can use the forward difference formula
for numerical differentiation and get a more accurate
approximation.
![]()
![[Graphics:../Images/CauchyRiemannMod_gr_59.gif]](../Images/CauchyRiemannMod_gr_59.gif)
![[Graphics:../Images/CauchyRiemannMod_gr_60.gif]](../Images/CauchyRiemannMod_gr_60.gif)
Note. In this case
the approximation is exact and the error is zero. This is
because
is a polynomial of degree less than 3.
Aside. If we want
to use a function for which the numerical approximation is not exact,
then
will
suffice.
![[Graphics:../Images/CauchyRiemannMod_gr_64.gif]](../Images/CauchyRiemannMod_gr_64.gif)
![[Graphics:../Images/CauchyRiemannMod_gr_65.gif]](../Images/CauchyRiemannMod_gr_65.gif)