Exercise Solution 2.18

The Jacobian of f is given by

[s1]

We can solve this problem by valuing each of the four derivatives—analytically or using finite differences—individually. Solutions are:

1. The analytic solution is

   [s2]

   

   [s3]

   

2. The central approximation matches the analytic solution to the number of decimal places indicated.

   [s4]

   
3. The forward approximation is not as good:

   [s5]