Ming Gu, Professor of Mathematics

Math 128A, Numerical Analysis, Spring 2012.

Required Textbook
- 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. Our goal is to cover the first 6 chapters of this book.
Matlab
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 is specifically taylored for Math 128 students. The class times and cnn's for Math 98 are
- Section 14 : MW 8:00 - 9:30, CCN 54191
- Section 15 : MW 9:30 - 11:00, CCN 54194
The first class will be held next Monday, Jan. 23.
Course Description for Math 98: (from Math 98 Instructor Cinna Wu)

This is a five week P/NP supplementary Matlab programming course for Math 128A. No prior programming experience is needed. We will cover the basics of Matlab needed to complete programming assignments in Math 128A. Classes will be held twice a week for 1.5 hours each. There will be five homework assignments and no exams. The course will cover writing functions in Matlab, working with vectors and matrices in Matlab, 2D and 3D plotting in Matlab, etc.

If you would like to enroll or to know more about this class, please contact Cinna Wu at cinnawu@math.berkeley.edu or visit /~cinnawu/math98.html .
Reference Implementation
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 However, their matlab programs are primitive and out of date, and can only be used as a reference.
Computer Accounts
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.
Waiting List
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, sooner or later.
Instructor
Prof. Ming Gu
Office: Evans 861
Office Hours: MWF 2:00-3:00PM; or by appointment.
Phone: 642-3145
Email: mgu@math
GSIs
- Jed Duersch
  send Jed email at jduersch@gmail.com.
  Discussion sections 101 (Tu 8:00-9:00AM), 102 (Tu 9:00-10:00AM), and 107 (Tu 2:00-3:00PM) B3 Evans.
  Office Hours MF 12:30-2:00PM at B3A Evans
- Alex Rennet
  send Alex Rennet email at rennetad@math.berkeley.edu.
  Discussion sections 103 (Tu 10:00-11:00AM) and 106 (Tu 1:00-2:00PM), B3 Evans.
  Office Hours: M 1:00-3:00PM at 1057 Evans.
- Christopher Peterson
  send Christopher Peterson email at peterson@math.berkeley.edu.
  Discussion sections 104 (Tu 11:00-12:00PM) and 105 (W 12:00-1:00PM), B3 Evans.
  Office Hours: Th 11:00AM-1:00PM at 1042 Evans.
Prerequisites
The prerequisites are Math 53 and 54 or equivalent. If you have doubts about them, please come talk with the instructor.
Course Work and Grading
There are a total of 100 points you can earn toward your final grade in the course. There will be up to 12 homeworks, 5 quizzes, 2 programming assignments, 1 midterm exam, and 1 final exam. We will only count the best 10 homeworks, best 4 quizzes towards your final grade, with each homework worth 1 point, and each quiz 2.5 points. Each programming assignment is worth 10 points. The midterm is worth 25 points and the final 35 points.

We will give no credit for written homework and programming assignment turned in after the due date and there will be no make up quizzes and exams. In case you have to miss the midterm exam, your final will be worth 60 points. You fail the class if you do not take the final exam.

Here are the quiz and exam dates:
- Quiz: Jan. 31 in discussion
- Quiz: Feb. 14 in discussion
- Midterm: Mar. 7 in class
- Quiz: Mar. 13 in discussion
- Quiz: Apr. 3 in discussion
- Quiz: Apr. 17 in discussion
The programming assignments will be due on Feb. 28 and Apri. 24, respectively.
Homeworks and programming assignments will involve written assignments to be done individually, although group discussion is allowed. Basic programming skills will be needed in both homework and programming assignments. The GSIs and myself will offer help for languages we are familiar with (mostly matlab.)

There will be no class performance curve. Your final letter grade will be determined based on the total number of points you earn in the class. Below is a list of cut-offs.
- A- to A+: at least 85 points
- B- to B+: between 70 and 85 points
- C- to C+: between 60 and 70 points
- D: between 55 and 60 points
- F: less than 55 points
In general the absolute majority of the class will get A and B level grades. To get a good grade, make sure you do your homework and programming assignments on time, and prepare well for your quizzes; your total exam scores (60 points) alone will only give you a C-.

Grades of Incomplete will be granted only for dire medical or personal emergencies that cause you to miss the final, and only if your work up to that point has been satisfactory.
Exams and Solutions
- Sample Final Exam for Spring of 2012.
- Sample Midterm for Spring of 2012.
- Midterm Exam used in Spring of 2008. Here are the Solutions.
- Sample Midterm II used in 2008. Here are selected Solutions.
- Final, Spring 2008.
Homework and Programming Assignments
- Homework Assignment #1 , Due Jan. 24, 2012 in discussion.
- Homework Assignment #2 , Due Jan. 31, 2012 in discussion.
- Homework Assignment #3 , Due Feb. 7, 2012 in discussion.
- Homework Assignment #4 , Due Feb. 14, 2012 in discussion.
- Homework Assignment #5 , Due Feb. 21, 2012 in discussion.
- Homework Assignment #6 , Due Feb. 28, 2012 in discussion.
- Homework Assignment #7 , Due March 6, 2012 in discussion.
- Homework Assignment #8 , Due March 13, 2012 in discussion.
- Homework Assignment #9 , Due March 20, 2012 in discussion.
- Homework Assignment #10 , Due April 3, 2012 in discussion.
- Homework Assignment #11 , Due April 10, 2012 in discussion.
- Homework Assignment #12 , Due April 17, 2012 in discussion.
- Homework Assignment #13 , Due April 24, 2012 in discussion.
- Homework Assignment #14 . Do not hand in.
- Programming Assignment #1 , Due Feb. 28, 2012 by 11:59PM. Please follow the submission instructions in the assignment.
- Programming Assignment #2 , Due April 26, 2012 by 11:59PM. Please follow the submission instructions in the assignment.
- matlab code to generate test cubics for Programming Assignment #1 .
- matlab code to generate test functions for Programming Assignment #2 . Note that testcase(6) is a very hard problem and problems this hard will NOT be used in our program tester. These test cases were generated by Jed.
Matlab Codes
- Chapter 1
- Chapter 2
  - Driver for bisection, fixed-point, and Newton .
  - bisection .
  - secant method .
  - 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:
- An ODE demo program that demonstrates how the following methods work on a sample problem :
- 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