Physics 780.20: Assignment #4

• Note that there are already functions defined that evaluate the first derivative of the cubic spline. Just use them.
• Problem 2 asks for a derivative to be accurate to 1e-6 as an absolute error in the region from 1 < r < 4. That means that the error shouldn't be greater than 1e-6 anywhere in that interval. It is sufficient to provide a well-labeled graph that shows how many points are required. (You should find roughly the minimum number of points that satisfies the condition.)
• You graph for part 5 on problem 3 should include the test data with error bars and the fit line.
• There are many ways to add parameters besides the example given; e.g., multiply by one plus a coefficient times some power of t.
• Make sure you modify both the function that calculates the residuals (expb_f) and the function that calculates the Jacobian (expb_df).