Math 128A, Numerical Analysis, Fall 2008.

• Class Information
  • Grade Distribution of Midterm II
  • We will most likely be able to cover all of Chapters 6 and 7 in the remaining 4 weeks of this semester (Nov. 14).
  • Section 5.8 will be skipped.
  • Most of the algorithms discussed in the text book have been implemented in various programming languages by the authors. These programs, including Java demos, are accessible at the Numerical Analysis Programs site. However, their matlab programs are very old and primitive. They can be used as references; but we can't depend on them.
  • For those who would like to have a copy of the homework solutions, please go talk with your GSIs.
  • DSP students: Your exam will be in 966 Evans, from 2:00-4:00PM.
  • I have postponed the due date for Hwk in section 3.2 to Oct. 1.
  • If you do not know it, you can ask your GSI or myself about the username and password on your computer account in the basement computer lab.
  • Review on Friday, Sept. 19, in Room 390, Hearst Mining, from 5:00PM to 6:00PM.
  • Midterm I will cover all material through Section 3.1.
  • People on the waiting list have to find an open discussion as soon as possible if you want to enroll in the class. This can be done on TeleBears.
  • General information about the course can befound here . See new info on recommended text for Matlab programming.
  • A syllabus can be found here . This document is where weekly homework and reading assignments can be found. Homeworks are collected Wednesdays during discussion. Note that homework due Oct. 8 has been updated (Oct. 3)
• Exams and Solutions
  • Sample Midterm: Midterm Exam used in Spring of 2008. Here are the Solutions.
  • Sample Midterm II. Here are selected Solutions.
  • Final, Spring 2008.
• Programming Homework
  • Programming Assignment #1 , Due Oct. 1, 2008 by 11:59PM. Please follow the instructions in the assignment regarding input and output format as well as how to submit your assignment.
  • Programming Assignment #2 , Due Oct. 29, 2008 by 11:59PM. Please follow the instructions in the assignment regarding input and output format. Email your program to Scott Armstrong.
  • Programming Assignments #3 and #4, Due Nov. 19, 2008 by 11:59PM. Please follow the instructions in the assignment regarding input and output format. Email your program to Scott Armstrong.
  • Programming Assignments #5, Due Dec. 10, 2008 by 11:59PM. Please follow the instructions in the assignment regarding input and output format. Email your program to Scott Armstrong.
• Matlab Codes
  • For those interested, this is a matlab code written by Eric Keldrauk for simulating the orbits of the sun and the earth which also carries a moon.
  • Gaussian Elimination with complete pivoting.
  • Gaussian Elimination with partial pivoting.
  • Kahan matrix.
  • A stiff ODE demo program that demonstrates usage of the Implicit Trapezoidal method with Newton Iteration:
    • Implicit Trapezoidal method with Newton Iteration;
    • test function and its
    • partial derivative .
  • An ODE demo program that demonstrates how the following methods work on a sample problem :
    • Explicit Runge-Kutta 4th order method ; vector version ;
    • Runge-Kutta-Fehlberg method ; vector version
    • Adams 4th order Predictor-Corrector method ; vector version;
    • the Adams Variable Step-size PC method ; vector version.
  • Gaussian Quadrature nodes and weights for any given value of n.
  • Simpson's Rule.
  • Composite Simpson's Rule.
  • Adaptive Simpson's Rule.
  • A demo program that demonstrates how the different versions of Simpson's rule work on an example function .
  • NewtonDividedDifference.m generates the coefficients in Newton's Divided Difference method for polynomial interpolation; the polynomials are evaluated with EvaluateNDD.m
  • NewtonDividedDifference2.m generates the coefficients in Newton's Divided Difference method for Hermite interpolation; the polynomials are evaluated with EvaluateNDD2.m
  • ClampedSplines.m generates the coefficients for Clamped Splines, which in turn are evaluated with EvaluateClampedSplines.m Bug fix on Oct. 23.
  • ApproximationDemo.m is a demonstration program that does function approximation with interpolation, Hermite interpolation, and clamped splines. It calls all the above matlab codes.
• Web Links
  • Math 98 homepage, taught by Maxim Trokhimtchouk in Spring 2008. In particular, Maxim has listed the topics he covered in his class and his homework assignments.
  • A brief history of numerical analysis.
  • A list of famous disasters caused by numerical mistakes.
  • Renaissance Technologies.
  • SPICE, a general-purpose circuit simulation program.