Math 128A, Numerical Analysis, Fall 2015.

• Required Textbook
  • R. L. Burden and J. D. Faires, Numerical Analysis, 9-th edition, 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/fall2015.html

  MATLAB will be available

  • During discussion sections in the computer lab B3A Evans
  • On computers owned by the university, UC Berkeley Software Central provides MATLAB for free
  • The Mathworks provide student editions of MATLAB at a discounted rate

• 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: TuTh 3:30-4:30PM, W 2:00-3:00PM; or by appointment.
  Phone: 642-3145
  Email: mgu@math
  

• GSIs
  
  • Danny Hermes
    send Danny Hermes email at dhermes@berkeley.edu.
    Discussion sections 102 and 103; Office hours 12-2:00PM Wed., 1040 Evans
    

  • Oran Gannot
    send Oran Gannot email at ogannot@berkeley.edu
    Discussion sections 104 and 105; Office hours TBA
    

  • Meire Fortunato
    send Meire Fortunato email at meirefortunato@berkeley.edu.
    Discussion sections 106 and 107; Office hours 10:00AM-Noon Wed., 1040 Evans
    

  • Qiuyi Zhang
    send Qiuyi Zhang email at 10zhangqiuyi@berkeley.edu.
    Discussion sections 108 and 109; Office hours Wed. 1:00-3:00PM
    

• 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: Sep. 9 in discussion
  • Quiz: Sep. 23 in discussion
  • Quiz: Oct. 7 in discussion
  • Midterm: Oct. 13 in class
  • Quiz: Oct. 21 in discussion
  • Quiz: Nov. 4 in discussion
  • Final Exam: Dec. 16, 8:00-11:00AM (Exam Group 9)

  The programming assignments will be due on Oct. 21 and Dec. 2, 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
  • Practice Midterm .
  • Practice Final Exam.
• Homework and Programming Assignments
  • Homework Assignment #1 , Due Sep. 9, 2015 in discussion.
  • Homework Assignment #2 , Due Sep. 16, 2015 in discussion.
  • Homework Assignment #3 , Due Sep. 23, 2015 in discussion.
  • Homework Assignment #4 , Due Sep. 30, 2015 in discussion.
  • Homework Assignment #5 , Due Oct. 7, 2015 in discussion.
  • Homework Assignment #6 , Due Oct. 14, 2015 in discussion.
  • Homework Assignment #7 , Due Oct. 21, 2015 in discussion.
  • Homework Assignment #8 , Due Oct. 28, 2015 in discussion.
  • Homework Assignment #9 , Due Nov. 4, 2015 in discussion.
  • Homework Assignment #10 , Due Nov. 10, 2015 in class.
  • Homework Assignment #11 , Due Nov. 18, 2015 in discussion.
  • Homework Assignment #12 , Due Dec. 2, 2015 in discussion.
  • Homework Assignment #13 , Do not hand in.
  • Programming Assignment #1 , Due Oct. 21, 23:59PM.
  • Programming Assignment #2 , Due Dec. 2, 23:59PM.
• 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.