Math 467 Numerical Analysis Spring 2005

• Syllabus
• Exploring Numerical Methods, Peter Linz and Richard Wang

Homework Assignments: (Listed by date assigned)

• Jan 18:
  1. Implement the Matlab code for the Riemann sum of a function using (a) Left hand heights, (b) Right hand heights
  2. Problems 2, 8 on p. 8-9
• Jan 19:
  1. Problems 2, 3, 6, 7 on p. 13 (Base conversions)
  2. Problem 9, p. 17
  3. Quiz 1- Online, turn in on Friday
• Jan 21: Read Cleve Moler's article. Problem 5, 11 p. 24
• Jan 25: What is zero? What is 1? Taylor's Theorem (with Remainder)
• Jan 27: (Solving Linear Systems) Prepare an algorithm to solve linear systems of equations
• Jan 28: Finish the algorithms in Matlab (Meet in the Math Lab)
• Feb 01: Work through the Least Squares examples in Matlab. The Worksheet is HERE
• Feb 03: See Friday's lab
• Feb 04: Friday lab is here
• Feb 08: Still working over 3.4 and 3.5-Let's finish this week!
• Feb 10: In Class Problems. Work through as much as you can, we'll try to finish Chapter 3 on Tuesday.
• Feb 11: Finish up Last Friday's Lab.
• Feb 15: Finish up the In Class Problems.
• Feb 17: Introduce Chapter 4: Polynomials. HW: Read Lagrange Polys for the Lab.
• Feb 18: Lab Day on Polynomials, Vandermonde Matrices, and Errors.
• Feb 22: Work on your lab. Let's try to finish up on Friday. Here are our new in-class problems to start working on.
• Feb 24: Work on the in-class problems.
• Feb 25: Finish up the lab from last Friday (Due Tuesday)
• Mar 01: Global polynomial approximation (Summary and orthog polys)
• Mar 03: Finish up orthog polys, start on cubic splines
• Mar 04: Lab on Cubic Splines and Orthog Polynomials. The data set is HERE as unknown1.mat. This contains vectors $xt$ and $yt$.
• Mar 8: Numerical Differentiation (6.1) Exercise 4, 7 for Thursday. Exercise 3 will be done in class. Also, write a script file that will implement the 3-point formula for derivatives.
• Mar 10: Fire Alarm went off today-
• Mar 11: Lab Due Today.
• Spring Break!
• April 1st Lab: Legendre Polynomials and Quadrature.
• April 8th: Continue with the April 1st Lab
• April 15th Lab: Roots and Newton's Method
• Apr 15-Apr 29: Solving Nonlinear Equations and Minimizing Functions
• Matlab (TestFor1.m) script to see the differences between "break" and "continue"
• Amoeba File
• Sample Functions for Amoeba

Chapter 1 Links

• Example: Roundoff Error can build up!

Chapter 2 Links

• A note on base-k conversions by hand.
• Our first quiz (due on Friday)
• Homework Link: Floating Point Representations, By Cleve Moler (of Matlab)

Chapter 3 Links

• A Short Example: Is the change in a solution to Ax=b due to numerical error, or is it a property of the matrix itself?

Chapter 5 Links

• NOTES ABOUT PPVAL and SPLINES

Chapter 7 Links

• Newton's Method in the Complex Plane (M-file. See the Lab, April 15th)

Final Exam Links

DEADLINE: TUESDAY MAY 17th

• Final Exam
• M-file for the D.E.s of the torus
• Sample M-file that creates a path and plots it on the surface of a torus
• Extra: Maple worksheet computing an arc and the arclength, with a plot of the torus. (This is the worksheet referred to in the Final Exam discussion)

Misc Links on Solving ODEs

• Examples of Solving ODEs in Matlab
• LaTeX file of the above, handy for Cut/Paste

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
• Actually, this disaster was due to bad number sense: Nobody noticed that the doseages administered were 10 times the normal amount (missing decimal point). CLICK HERE