Math 128A, Numerical Analysis, Spring 2017.

• Required Textbook
  • R. L. Burden and J. D. Faires, Numerical Analysis, 9-th/10-th editions, Brooks-Cole, 2011.
  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. I encourage you to take it if you would like to learn more about Matlab. For more details, please see math.berkeley.edu/~cpoli/math98/spring2017.html

  MATLAB will be available

  • During discussion sections in the computer lab B3A Evans.
  • The Mathworks provide student editions of MATLAB at a discounted rate.

  You can also try the freely available software package Octave. Be aware that the Octave syntax is largely, but not completely, compatible with Matlab.

• 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: TuWTh 1:30-3:00PM, or by appointment.
  Phone: 642-3145
  Email: mgu@math
  

• GSIs
  
  • Danny Hermes
    send Danny Hermes email at dhermes@berkeley.edu.
    Discussion sections 104, 107 and 109; Office hours TBA
    

  • Chen Shen
    send Chen Shen email at chenshen@berkeley.edu
    Discussion sections 102, 103 and 106; Office hours TBA
    

  • Ruochen Liang
    send Ruochen Liang email at liangrc2012@berkeley.edu.
    Discussion sections 101, 105 and 108; 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 up to 14 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/Feb. 1 in discussion
  • Quiz: Feb. 14/Feb. 15 in discussion
  • Programming Assignment 1: 11:59PM, Feb. 22
  • Quiz: Mar. 7/Mar. 8 in class
  • Midterm: Mar. 21 in class
  • Quiz: Apr. 4/Apr. 5 in discussion
  • Quiz: Apr. 18/Apr. 19 in discussion
  • Programming Assignment 2: 11:59PM, Apr. 28
  • Final Exam: May 12, 7:00-10:00PM ( Exam Group 20)

  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.
  

• Lecture Notes (read the book, lecture notes do not cover everything)
  • Lecture notes for week of Jan. 16
  • Lecture notes for week of Jan. 23
  • lecture notes for week of jan. 30.
  • lecture notes for week of Feb. 6.
  • lecture notes for week of Feb. 13.
  • lecture notes for week of Feb. 20.
  • lecture notes for week of Feb. 27.
  • lecture notes for week of March 6.
  • lecture notes for week of March 13.
  • lecture notes for week of March 20.
  • lecture notes for week of April 3.
  • lecture notes for week of April 10.
  • lecture notes for week of April 17.
  • lecture notes for week of April 24.
• Exams and Solutions
  • Practice final exam
• Homework and Programming Assignments
  • Homework Assignment #1 , Due Jan. 25, 2017 by 11:59PM.
  • Homework Assignment #2 , Due Feb. 1, 2017 by 11:59PM.
  • Homework Assignment #3 , Due Feb. 8, 2017 by 11:59PM.
  • Homework Assignment #4 , Due Feb. 15, 2017 by 11:59PM.
  • Homework Assignment #5 , Due Feb. 22, 2017 by 11:59PM.
  • Homework Assignment #6 , Due March 1, 2017 by 11:59PM.
  • Homework Assignment #7 , Due March 8, 2017 by 11:59PM.
  • Homework Assignment #8 , Due March 15, 2017 by 11:59PM.
  • Homework Assignment #9 , Due March 22, 2017 by 11:59PM.
  • Homework Assignment #10 , Due April 5, 2017 by 11:59PM.
  • Homework Assignment #11 , Due April 12, 2017 by 11:59PM.
  • Homework Assignment #12 , Due April 19, 2017 by 11:59PM.
  • Homework Assignment #13 , Due April 26, 2017 by 11:59PM.
  • Homework Assignment #14 , Do not hand in.
  • Programming Assignment #1 , Due 23:59PM, Feb. 22, 2017.
  • Programming Assignment #2 , Due 23:59PM, April 28, 2017.
• Matlab Codes
  • Chapter 1
    • Displaying underflow and overflow threshold .
    • Fixed digit arithmetic.
    • Computing quadratic root with Vieta's formula.
    • Horner's method.
  • 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:
    • 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.
  • 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.
  • SPICE, a general-purpose circuit simulation program.