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]

 

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