This assignment will test your understanding in obtaining approximate formulae and their errors for numerical derivatives. You have to obtain the numerical coefficients of the 5-point approximation formula for the second order derivative (Eq. [6] in the DERIVATIVES handout). You can do the calculations by hand or using MATHEMATICA for the 5-point second order derivative. You should also calculate the leading order of the error term. Details of the calculations are required.
Test the above approximation in a FORTRAN code similar to der.f which can be found in the /home/tomanek/PHY480/HW3 directory on gauss. You are required to use the function
for this test.
Please, include both a copy of the code and your results in your report.