Math 128A (late morning) Summer 2009

General Information

Registration Information: Lecture CCN: 58840; , Section CCN: 58845; Enrollment information: via Info-BEARS

Instructor: Justin Blanchard, 1008 Evans, .

Location/time: 9 Evans, Mon.-Thurs. 10:00-12:00 Berkeley Standard Time

Instructor office hours: 1008 Evans, Mon. 12-1, Wed. 2-3, Fri. 4-5, or by appointment.

Lab GSI: Kazi,

Lab location/hours: 106 Latimer Hall, Tues.-Fri. 12:00-2:00 (ask instructor for username and password!)

Lab GSI office hours: 1042 Evans, Mon. 1-2, Thu. 2:30-3:30

Announcements

• 2009/08/04: PA3 is out! Due date will be Wednesday 4/12. euler.m and rk4.m have been updated to work better when f(t,y) spits out a column vector, which may help with a HW7 problem. HW7 typos have been corrected.
• 2009/07/28: PA2 is out! It's due in a week (on Tuesday).
• 2009/07/21: This week's HW (#5) may be turned in by office hours on Friday.
• 2009/07/16: Revised MT2 date is Tuesday 7/28. Format will be similar to MT1; coverage is up to section 5.5.
• 2009/07/09: PA1 is out. Due date is Monday 7/20.
• 2009/07/03: Office Hours: I had forgotten that Evans would be locked today. I'll still be available, but outside Evans (first floor, west side -- there will be signs on the doors). I apologize for the inconvenience. Homework 3: There is homework due after the midterm. It is short (5 problems) and all questions are suitable as midterm study problems. Midterm 1: It will cover 1.1 to 3.2; all questions will be similar to homework questions. There will be 5 problems and a one-hour time limit. Closed-book, closed-notes. Resources other than Monday's review include the actual and sample MT1 exams from last spring's web page. MT1 will be followed by a mid-term course evaluation, your first chance to grade me. Any feedback will be appreciated. Thanks, Justin
• 2009/06/22: In place of a quiz, the first week will feature a survey. This is intended to help me set office hours and the direction of the course.

Resources

Required

Textbook: Numerical Analysis, 8th Edition (2005) by Burden and Faires

Software: MATLAB 7 (R14) or later (version R2008a available in lab), or alternatively the free and open-source QtOctave (Win / Linux x86 / source code). Correct code written for 128A should run equally well in either system. MATLAB will be the official language for programming assignments in this class; it is easier to use and often installed in research and academic settings. QtOctave, a graphical interface to Octave, allows the use of a very similar language. If you own a computer and wish to work outside lab hours without buying MATLAB, you may find it useful. Berkeley students can buy MATLAB here (in the second week of class); students in general can look here.

Code

2.1: bisection.m, bisection_table.m

2.2: fixedpoint.m, fixedpoint_table.m

2.3: newton.m, newton_table.m; secant.m, secant_table.m; false_position.m, false_position_table.m

2.5: steffensen.m, steffensen_table.m

2.6: horner.m; muller.m, muller_table.m

3.1: neville.m, neville_table.m

3.2: divided_difference_table.m, divided_difference_coefs.m

3.3: hermite_table.m, hermite_coefs.m

PA1: newton_eval.m

5.2: euler.m

5.4: rk4.m

5.5: rkf.m

PA2: plot_parabola.m

Links

Matrix algebra handout (from spring)

Math 128A Summer 2009, Benjamin Johnson

Math 128A Spring 2009, Per-Olof Persson

Math 128A Fall 2008, Ming Gu

Math 128A Spring 2008, Ming Gu

Math 128A Spring 2008, Ming Gu

MATLAB Online Documentation

Assignments, Grading, Collaboration

Your grade will be determined by a combination of the following assignments. Individual assignments may be "curved" before being counted toward final grades.

• Homework (15%): Assigned on Fridays (except on the first week) and collected at the end of discussion on Thursdays. Collaboration is allowed and encouraged, but any work you turn in must be your own. Late homework will not be accepted for non-emergency reasons, but the two lowest homework scores will be dropped.
• Quizzes (10%): Brief, two-to-four question quizzes will be given on Tuesdays during discussion. Collaboration is not allowed. No make-up quizzes will be given, but the lowest two scores will be dropped.
• Programming Assignments (3 x 5%): Same collaboration policy as homework. Details TBA.
• Midterms (2 x 20%), Final (20%): These will be in-class, closed-notes, closed-calculator. Missing a midterm will make your final exam grade worth more, and is not recommended.

Tentative Schedule

Note: The exam dates below are insane and will definitely change.

Date	Topics	Reading	Assignments due
Mon. 06/22	Review of calculus, computer arithmetic	1.1, 1.2
Tue. 06/23	Computer arithmetic, discussion	1.3	survey
Wed. 06/24	Algorithms and Convergence, Bisection Method	2.1, 2.2
Thu. 06/25	Newton's Method, discussion	2.3	HW1, Solutions
Mon. 06/29	Error Analysis for Iterative Methods, Accelerating Convergence	2.4, 2.5
Tue. 06/30	Zeros of Polynomials and Muller's Method, discussion	2.6	Quiz 1, Solutions
Wed. 07/01	Interpolation and the Lagrange Polynonial, Divided Differences	3.1, 3.2
Thu. 07/02	Hermite Interpolation, discussion	3.3	HW2, Solutions
Mon. 07/06	Cubic Spline Interpolation, (see book)	3.4, review
Tue. 07/07	Midterm 1	Up to 3.2	MT1, Solutions
Wed. 07/08	Numerical Differentiation, Richardson's Extrapolation	4.1, 4.2
Thu. 07/09	Elements of Numerical Integration, discussion	4.3	HW3, Solutions
Mon. 07/13	Composite Numerical Integration, Romberg Integration, Adaptive Quadrature	4.4, 4.5, 4.6
Tue. 07/14	Gaussian Quadrature, discussion	4.7	Quiz 2, Solutions
Wed. 07/15	Multiple Integrals, Improper Integrals	4.8, 4.9
Thu. 07/16	Review of integration / discussion	Ch. 4	HW4, Solutions
Mon. 07/20	Theory of Initial-Value Problems, Euler's Method	5.1, 5.2	PA1, Solutions
Tue. 07/21	Higher-Order Taylor Methods, discussion	5.3	Quiz 3, Solutions
Wed. 07/22	Runge-Kutta Methods, Error Control / Runge-Kutta-Fehlberg Method	5.4, 5.5
Thu. 07/23	Multistep Methods, discussion	5.6	HW5, Solutions
Mon. 07/27	Midterm practice	Up to 5.5
Tue. 07/28	Midterm 2	Up to 5.5	Practice; MT2, Solutions
Wed. 07/29	Variable Step-Size M.S. Methods, Extrapolation Methods, Higher-Order ODEs and Systems of ODEs	5.8-5.10
Thu. 07/30	Stability, Stiff Differential Equations (may not finish!), discussion	5.10, 5.11	HW6, Solutions
Mon. 08/03	Linear Systems of Equations, Pivoting Strategies		6.1, 6.2
Tue. 08/04	Linear Algebra and Matrix Inversion, discussion	6.3	PA2
Wed. 08/05	Determinants, Matrix Factorization	6.4, 6.5
Thu. 08/06	Special Types of Matrices, discussion	6.6	HW7, Solutions
Mon. 08/10	Special types of matrices	7.1, 8.1
Tue. 08/11	Vector and Matrix Norms	8.2	Quiz 4, Solutions
Wed. 08/12	Review		PA3, Solutions
Thu. 08/13	Final	1.1-7.1	Exam (Review problems, Solutions)