Assignment #2

Assignment Problems (Click on the link to view PDF):

Sample Codes and Illustration :

  1. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/NL_sys_solver
    Learn how to use Newton's method to solve a non-linear system.

  2. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/Num_cancel
    See the bad effect of numerical cancellation and the way to avoid it.

  3. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/Uncertainty
    Learn how to calculate the statistical uncertainty in an estimated parameter. Also learn how to plot a histogram.

  4. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/Total_error
    See how the total error changes with the step size "h". In particular, when "h" is below certain value, the total error actually increases as "h" decreases! Compare the results by the first order method, the second order method and the fourth order method. Notice that the fourth order method attains the minimum total error at a fairly large step size. Also the minimum total error attained by the fourth order method is much smaller that that by the first order method.

  5. Download and run the Matlab codes in
    http://www.cse.ucsc.edu/~hongwang/Codes/Num_integration
    See how the codes work and learn how to implement composite Trapezoidal rule, composite Simpson's rule and composite Gaussian integration.