Math 128A, Numerical Analysis, Fall 2010.

• Class Information
  • Run this matlab program for Midterm II stats.
  • The homework problems in Chapter 5 (ODEs) become very tedious if done by hand. Download the ODE demo program to play with various ODE matlab routines on this site before you do your homework. They can help solve your homework problems much more quickly.
  • We will skip section 5.8.
  • Run this matlab program for Midterm I stats.
  • We will skip section 3.2 in 9th edition, and the corresponding material in section 3.1 of 8th edition ( Neville's Method.) We will also skip the section on parametric curve in Chapter 3.
  • The required textbook is
    • R. L. Burden and J. D. Faires, Numerical Analysis, 9-th edition, Brooks-Cole, 2011.
    However, due to the high cost of the textbook, you are allowed to use the 8th edition instead. We will try our best to minimize any potential problems when lecturing and assigning homework problems.
  • Matlab is going to be the programming language for this class. Good matlab programming skills can go a long way to earn you a descent grade in this class. The Math Department offers a 1-credit class Math 98 this semester to help those who want to learn or enhance their matlab skills. This class lasts for about 5-6 weeks, and is specifically taylored for Math 128A students. If you would like to enroll or to know more about this class, please contact Boris Ettinger at ettinger@math.berkeley.edu or visit /~ettinger/math98.html .
  • 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.
  • If you do not yet know it, you can ask your GSI or myself about the username and password on your computer account in the basement computer lab.
  • 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.
  • More Details
    • More general information about the course can befound here .
  • 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.
  • Homework and Programming Assignments
    • Homework Assignment #1 , Due Sept. 8, 2010 in discussion.
    • Homework Assignment #2 , Due Sept. 15, 2010 in discussion.
    • Homework Assignment #3 , Due Sept. 22, 2010 in discussion.
    • Homework Assignment #4 , Due Sept. 29, 2010 in discussion.
    • Homework Assignment #5 , Due Oct. 6, 2010 in discussion.
    • Homework Assignment #6 , Due Oct. 13, 2010 in discussion.
    • Homework Assignment #7 , Due Oct. 20, 2010 in discussion.
    • Homework Assignment #8 , Due Oct. 27, 2010 in discussion.
    • Homework Assignment #9 , Due Nov. 3, 2010 in discussion.
    • Homework Assignment #10 , Due Nov. 10, 2010 in discussion.
    • Homework Assignment #11 , Due Nov. 17, 2010 in discussion.
    • Homework Assignment #12 , Due Nov. 24, 2010 in discussion.
    • Homework Assignment #13 , Due Dec. 1, 2010 in discussion.
    • Programming Assignment #1 , Due Sept. 29, 2010 by 11:59PM. Updated Sept. 24, 2010. 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. 27, 2010 by 11:59PM.
    • Programming Assignment #3 , Due Nov. 24, 2010 by 11:59PM.
    • Programming Assignment #4 , Due Dec. 8, 2010 by 11:59PM.
  • Matlab Codes
    • Matlab Driver for rootfinders.
      • Driver for bisection, fixed-point, and Newton .
      • bisection .
      • fixed-point .
      • Newton .
      • Test function for Bisection and Newton, derivative for Newton, and fixed point function for fixed point method.
    • Polynomial Interpolation routines.
      • Tester for Polynomial Interpolation.
      • NewtonDividedDifference.m generates the coefficients in Newton's Divided Difference method for polynomial interpolation.
      • The polynomials are evaluated with EvaluateNDD.m
    • Hermite Interpolation routines.
      • Tester for Hermite Interpolation.
      • NewtonDividedDifference2.m generates the coefficients in Newton's Divided Difference method for Hermite interpolation.
      • The polynomials are evaluated with EvaluateNDD2.m
    • Simpson's Rule
      • Demo program that demonstrates how the different versions of Simpson's rule work on example functions. You need to download related codes for the demo to work.
      • Simpson's Rule.
      • Composite Simpson's Rule.
      • Adaptive Simpson's Rule.
      • test function.
    • Gaussian Quadrature nodes and weights for any given value of n.
    • 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.
    • 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
    • A brief history of numerical analysis.
    • A list of famous disasters caused by numerical mistakes.
    • Renaissance Technologies.
    • SPICE, a general-purpose circuit simulation program.