Ming Gu, Professor of Mathematics

Math 128A, Numerical Analysis, Spring 2021.

Required Textbook
- R. L. Burden and J. D. Faires, Numerical Analysis, 10-th edition, Brooks-Cole.
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.
There is a one-credit Math98 course on basic Matlab that runs through the first 6 weeks of the semester. Andrew Shi is a great instructor and I encourage you to take it if you would like to learn more about Matlab.
MATLAB will be available by
- free download via https://www.mathworks.com/academia/tah-portal/berkeley-731130.html .
Instructor
Prof. Ming Gu
Office Hours: TuWTh 3:30-4:30PM; or by appointment.
Email: mgu@math
GSIs
- Michael Heinz, email michael_heinz@berkeley.edu; Office hours TBA
- Raehyun Kim, email rhkim79@berkeley.edu; Office hours TBA
- Izak Oltman, email ioltman@berkeley.edu; Office hours TBA
- Jiaming Wang, email jiaming_wang@berkeley.edu; Office hours TBA
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 13 homework sets, 6 quizzes, 1 programming assignment, 1 midterm exam, and 1 final exam.

You will earn up to 1.5 points per homework set and 3 points per quiz towards to your final grade, with the total homework and quiz points capped at 15 points each. Programming assignment is worth 20 points. The midterm is worth 20 points and the final 30 points.
We will give no credit for late class work and there will be no make up quizzes and exams. In case you have to miss the midterm exam, your final will be worth 50 points. You fail the class if you do not take the final exam.

Homework sets are in general due on Mondays (or Tuesday if Monday is a holiday.) Here are the quiz, project, and exam dates:
- Quiz: Feb. 3
- Quiz: Feb. 17
- Quiz: Mar. 3
- Midterm: Mar. 16 in class
- Quiz: Mar. 31
- Quiz: Apr. 14
- Programming Assignment: Due 11:59PM, Apr. 21
- Quiz: Apr. 28
- Final Exam: May 10, 11:30AM-2:30PM (Exam Group 2)
Homeworks and programming assignment will involve written assignments to be done individually, although group discussion is allowed. Basic programming skills will be needed in both homework and programming assignment. The GSIs and myself will offer help for languages we are familiar with (mostly matlab.)
Note that as long as the lectures remain online, all quizzes will be take-home, and there will be alternative exam times to accommodate students who are in different time zones.
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 (50 points) alone will only give you an F grade.

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.
Lecture Notes and Course Materials
- All lecture notes, handouts, homework sets, quizzes, and programming assignments are available on bcourses.
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.
  - A memory efficient version of Neville's method for polynomial interpolation.
  - Tester for Polynomial Interpolation.
  - NewtonDividedDifference.m generates the coefficients in Newton's Divided Difference method for polynomial interpolation.
  - A memory efficient version of 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
- Spline Functions
  - ClampedSplines.m generates the coefficients for Clamped Splines, which in turn are evaluated with EvaluateClampedSplines.m Here is testSplines.m that tests the Spline functions.
- 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 :
- 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