Math 467 Numerical Analysis Fall 2006

• Syllabus
• (Amazon.com link) Textbook

Homework Assignments: (Listed by date assigned)

1. HW Assigned Aug 30, 2006 (Due on Monday, Sep 4)
2. Homework 1 Solutions
3. HW Assigned Sep 4 (Due Sep 8)
4. Homework 2 Solutions
5. Homework 3: We're doing these in-class on 9/13, 9/15 and 9/18
• Homework 3 solutions done on 9/13
6. Homework 4 (to turn in): Exercises on Pages 5,6, 9, 10 of ``The Interpolation Problem''. (Due Friday, 9/29)
7. Homework 5 (to turn in Friday, Oct 20) (Note that this was handed out as Homework 4 instead of 5).
8. Homework 6: Problems 5.2, 1, 2, 3, 7, 10. Computer problems 5.2.6, 5.2.7 (Due Monday, Oct 30)
1. Homework 6 Solutions
2. Script File for the last Problem
3. M-file for Composite Trapezoidal Rule
4. M-file for Composite Simpson's Rule
9. Homework 7 (Chapter 6, Section 1)
1. A Quick Summary of some ODEs
2. Homework 7 solutions

Course Notes

1. Floating Point Computations
2. Rates of Convergence. Contains exercises for Homework Set 3. (Sep 11)
3. Notes on Error Analysis. Contains exercises for Homework Set 3. (Sep 13)
4. The Interpolation Problem (updated 9/26 to include 10 pages. Chebyshev polys were taken to the document below).
5. Chebyshev's Theorem
6. Cubic Splines (Oct 6 2005)
7. Differentiation and Integration: These are from the draft notes that say "Chapter 5"
• Example in Maple: Getting a forward difference formula for the second derivative
• Richardson Extrapolation Examples
• A Summary of Important Formulas
• Notes on Using Matlab's QUAD function

Matlab Materials

• An Intro to Matlab
• M-file for Bisection: bisect.m
• M-file for Fixed Point Iteration: fixpt.m
• An M-file for Newton's Method in the Complex Plane. The function is a generic cubic, z^3+az+b. The a, b values can be changed in the code. To see the nice picture, just download the file and run it in Matlab.
• M-file for the Wilkinson Polynomial: wilkpoly.m
• M-file for computing the Lagrange Polynomial: lagrange.m
• Files for Newton's Divided Differences:
• Horner's Method: nest.m
• Newton's Divided Differences: newtdd.m
• Chebyshev Example Script (M-file)
• Files for the Animated Pendulum: If you download the following, just run the main script file: PendScript. It will call the other functions.
1. Main Script File: PendScript.m
2. Animation function: animPend.m
3. The Pendulum ODE function: Pend1.m
4. Improved Euler Method: ImpEulerVec.m
• File for animating the double pendulum. To use this, obtain the numerical solution, vector t and matrix y, then in Matlab type: animDoublePend(t,y). The lengths of the rods are assumed to be 1, and g=9.8.
  Animation File: animDoublePend.m
  
• Files for the Tacoma Narrows Bridge Example:
  1. Program to do the Animation (AnimateBridge.m)
  2. The differential equations function (TacomaODE.m)

Death and Destruction from bad Numerical Analysis

• 28 Deaths and Billions of Dollars Lost
• Mars Orbiter crashes into Mars due to a missing metric conversion