PHYCS 6730 Lab Exercise

Pade approximant

1. Find the (4,2) Pade rational function approximation for 1/cos(x), so that it matches a Taylor series expansion about x = 0. Note that Maple will do it for you. For help, use ?Pade. To access the Pade command directly, start with the command with(numapprox);.
2. Do a Taylor series expansion of 1/cos(x) and the Pade approximation to check that Maple did it correctly.
3. Find the pole of the Pade approximation closest to x = 0, and compare with the known location of the corresponding pole in 1/cos(x).
4. Make a table comparing values of 1/cos(x) with the (4,2) Pade approximant and the 6th degree Taylor polynomial at the values shown:

           x      1/cos(x)    Taylor(6)  diff   Pade(4,2)   diff
           0.0
           0.2
           0.4
           0.6
           0.8
           1.0