HOMEWORK ASSIGNMENTS AND LABS :
AA214A

Thomas H. Pulliam

After the due date of an assignment the answers will be accessable
AA214A: Class assignments:
Assignment #1  Assignment #2 ---:--- Assignment #3 ---:--- Assignment #4 ---:---


Assignment #1 DATE: 09/21/2009 : Homework #1 Due DATE: 9/28/2009 :Lab
  • Lab 1: Stability Examples (Lab #1)
    Either type in the code directly to MATLAB or download the code to a file. Follow the instructions at the top of the assignment. Only turn in your written observations and figures.
    For those of you who can not get access to Matlab, here is a FORTRAN version of the assignment.
  • Lab 1: Stability Examples (Lab #1)
    discussion and results for this assignment.
    Also check out the supplemental handout
  • Supplemental Handout #1 [postscript 61Kb] ....[pdf format 59Kb]
    A Matlab demo of all the assignments from Lab1
    If you want to see an extended version of this project with a few extra twists and a fancy user interface check out
    Example1_m.m
    You will need the other files:
    Example1_m.mat
    project1_m.m
    instructions.m
    Type at prompt for matlab: Example1_m
    A Tar file of Example1_m


    Assignment #2 DATE: 09/28/2009 : Homework #2 DUE 10/05/2009
  • Problem Set #2 [pdf format]
  • Answer Sheet [pdf format]


    Lab Assignment #2 DATE:: Lab #2 DUE: Optional Assignment (Do Not Turn In)
  • Assignment:
    Run this example error analysis program and study the code to understand what is being done.
    Derive the Taylor Table Analysis for the Order of Accuracy for each of the methods used.
    Compare the analysis results with the numerical results obtained below. Try as many levels as your machine can reasonably handle, 12 levels would be good.
    Write a short (1-2 paragraph) explaination of what you observed.
  • Code: An example of the accuracy of various differerencing approximations to the first derivative. This is a Matlab program which defines a function and its derivative. It computes a first order one-sided, second order central and one-sided, and fourth order central 5pt and compact Pade differences. Error estimates show the accuracy convergence characteristics.
    An example of the resulting error analysis [postscript] [gif] .....[pdf format] is available,
  • Diff. Example: Example of Differencing Accuracy (Main code)
  • Support Routine
    Make sure to download both the above links, the Main code and the support routine !!!



    Lab Assignment #3 Date:: Lab #3 DUE Optional (Do not turn in)
  • Lab #3: Download or type in the code:
    Main routine for Lab #3
    Support routine for Lab #3
    Support routine for Lab #3
    Support routine for Lab #3
    Support routine for Lab #3
    You will need all 5 of the matlab files to run this Lab or you can type it in
    A Postscript Listing of Lab #3
    A pdf Listing of Lab #3
    A tar file of all the routines for easier downloading
    Assignment: Run the code for jmax = 31, exciting all the modes and total time = 100. Make observations as to what is happening to the various modes in time. Write a short discussion of your observations and explaination of what is happening.
    As a check for you, plots of the eigenvalues, decompostion coefficients C in bar graph and line format and the final solution is presented at t = 0.0 [postscript], .....[pdf format],
    t = 10.0 [postscript] .....[pdf format],and t = 100.0 [postscript] .....[pdf format].
    Note that with all the modes excited the initial C's are all 1. Try just one mode (say 3 and 20) and watch what happens. Since the high frequency (large m) eigenvalues are the largest negative values the high frequency transient components damp out first. The solution curve eventually is only made up of the low frequency eigenspectrum, which is made up of smooth eigenmodes. (The solution starts out pretty ragged and eventually smooths out.)

    Assignment #3 Date:10/13/09 : Homework #3 Due:10/26/09 ::
  • Homework 3.....[pdf format]
  • Answer for HMW 3.....[pdf format]


    Assignment #4 Date:11/09/09 : Homework #4 Due:11/18/09 ::
  • Homework 4.....[pdf format]
  • Answer for HMW 4.....[pdf format]


    Thomas H. Pulliam <thomas.h.pulliam@nasa.gov>