CS 111: Introduction to Computational Science: Fall 2007

Introduction to scientific computing, emphasizing basic numerical algorithms and the informed use of mathematical software. Matrix computation, systems of linear and nonlinear equations, interpolation and zero finding, differential equations, numerical integration. Students will learn and use the Matlab language.

Instructor:

• Email: gilbert@cs.ucsb.edu
  
• Office: Harold Frank Hall 5109
  
• Office hours: see my web page.

Teaching assistant:

• Email: alugowski@cs.ucsb.edu
  
• Office hours: Thursdays 3:00 to 5:00 pm in CSIL
  

Discussion and announcements:

There is a Google discussion group for the class at http://groups.google.com/group/ucsb-computer-science-111-fall-2007. All students are expected to join this group and to watch it for course announcements. You may also use it to post questions for the instructor and assistant (and answers to other people's questions). The mailing address for posting to the group is ucsb-computer-science-111-fall-2007@googlegroups.com.

Class meetings:

• Lecture: Monday and Wednesday 12:30-1:45, Trailer 387 (near Psych), room 101
  
• Discussion: Friday 2:00-2:50, Trailer 932

Textbook:

The textbook is: Numerical Computing with Matlab, by Cleve Moler. The book has a web site. Besides the bookstore, you can download the book from its web site, or you can order it from SIAM, the Society for Industrial and Applied Mathematics. You can get a discount on the book if you are a member of SIAM, which is free for UCSB students (talk to me).

Course software and computer resources:

You'll use Matlab for all your programming in the course. It works on the Linux computers in CSIL and on the Windows computers in the ECI labs. To run Matlab from your personal machine, you can log in to CSIL remotely and forward the graphics (instructions under construction), or else buy a copy of the "student version" at the bookstore.

The course will also use the "NCM" software, which you can put on your Matlab path at CSIL in any of several ways:

• at the Matlab prompt: addpath /cs/class/cs111/ncm
• in your startup.m file: addpath /cs/class/cs111/ncm
• when running Matlab: matlab -r "addpath /cs/class/cs111/ncm"
• bash command or put in ~/.bashrc: export MATLABPATH=/cs/class/cs111/ncm
• csh command or put in ~/.cshrc: setenv MATLABPATH /cs/class/cs111/ncm

For the ECI lab machines or your personal machine, you can download your own copy of NCM from the textbook web site.

Grades:

• Class participation: 15%
• Homework assignments: 40%
• Midterm exam: 15%
• Final exam: 30%

Midterm:

• Monday, November 5, in class
• Open book, open notes, no computers
• The midterm will cover chapters 1 and 2 of the text and general knowledge of Matlab including indexing, permutations, and so forth.
• The 2005 midterm. (CS 111 was called CS 110A in 2005.)

Final exam:

• Noon - 3:00 pm, Wednesday, December 12, in classroom
• Open book, open notes, no computers
• The final will cover material from the entire course. (See the list of topics.)
• The 2005 final. (You can ignore questions 5 and 6, which are topics we did not cover this year.)

Homework policy:

All homework must be submitted in hard copy, on paper. When a homework exercise requires a Matlab program, turn in four things:

• the program listing (m-files)
• the diary of your Matlab session running the program
• copies of any output figures or plots
• a description in English of what you did and how

If you have questions about grading of homework, talk to the t.a. first. If you are unable to reach an agreement, make an appointment to talk to me. The statute of limitations for regrades is one week -- that is, any requests for regrades must be made no later than one week after the homework (or exam) was returned in class.

Homework assignments:

• Due Wed, Oct 3: Do the review quiz. Turn this in, Wednesday in class. We will correct the quiz, but you will get full credit just for turning it in. Here is the answer key for the quiz.
• Due Mon, Oct 8: Exercises 1.1, 1.13, 1.15, 1.17. (Turn these in for a grade, in class.)
• Due Mon, Oct 15: Exercises 2.1, 2.4, 2.8, 2.10 (Turn these in for a grade, in class.)
• Self study for Mon, Oct 15: Exercises 2.3, 2.7, 2.17 (Don't turn these in, they are to test your own understanding.)
• Due Mon, Oct 22: Exercises 2.5, 2.16(a), 2.16(b), 2.16(d), 2.22, 2.23, 2.26 (Turn these in for a grade, in class.)
• Self study for Mon, Oct 22: Exercises 2.12, 2.14, 2.25 (Don't turn these in, they are to test your own understanding.)
• Due Mon, Oct 29: Exercises 2.18, 1.34, 1.36, 1.38 (Turn these in for a grade, in class.)
• Self study for Mon, Oct 29: Exercises 2.15, 1.35, 1.39 (Don't turn these in, they are to test your own understanding.)
• Self study for Mon, Nov 5: The 2005 midterm. (No homework is to be turned in for a grade Mon, Nov 5.)
• Due Wed, Nov 14: Exercises 5.2, 5.3, 5.8 (Turn these in for a grade, in class.) Hint for 5.3: Use the ``fzero'' function in Matlab.
• Due Mon, Nov 19: Exercise 5.11 (Turn this in for a grade, in class.) See also the NIST web page on this problem, and the original 1967 paper on it.

Note: Some older versions of the book have different problem numbers in Chapter 7. The following assignments are from the current online version of Chapter 7.
• Due Mon, Dec 3: Exercises 7.1 (standard form), 7.4 (erf), 7.16 (modified Lotka-Volterra), 7.17 (paratrooper). Turn these in for a grade, in class.
• Self study for Mon, Dec 3: Do all the examples in Section 7.7, pages 199-201, in Matlab (this won't take long). Also, do exercises 7.3 (BS23) and 7.6 (stiffness). Don't turn these in, they are to test your own understanding.
• Self study for the week of Dec 3: Exercises 7.12 (Lorenz attractor) and 7.18 (cannonball). Also please read exercise 7.21 (carbon dioxide), and play with it if you'd like. This is a long exercise, but it's a fairly realistic example of the use of ODEs in climate change research. Don't turn any of these in.

Reading assignments:

• Mon, Oct 1: Read Sections 1.1 through 1.6 of the text.
• Wed, Oct 3: Read Sections 2.1 through 2.7 of the text.
• Mon, Oct 8: Read Sections 2.8 through 2.12 of the text.
• Wed, Oct 17: Read Section 1.7 of the text, and Trefethen's essay on numerical analysis.
• Mon, Oct 29: Read Sections 5.1 through 5.3 of the text.
• Tue, Nov 6: Read Sections 5.4 through 5.7 of the text.
• Wed, Nov 14: Read Sections 7.1 through 7.4 of the text.
• Mon, Nov 26: Read Sections 7.5 through 7.12 of the text.
• Wed, Nov 28: Read Sections 7.13 and 7.14 of the text. (You won't be responsible for these sections on the exam, but it's useful to see what the issues in error analysis are.)

Class schedule, links, slides, and diaries:

• Mon Oct 1: Introduction. The fractal fern. [diary]

• Wed Oct 3: Systems of linear equations. [diary (you will also need to put the file temperature.mat in your home directory)]

• Mon Oct 8: LU factorization, pivoting. [diary]

• Wed Oct 10: Permutation matrices, permutation vectors, pivoting. [diary]

• Mon Oct 15: Guest speaker, Viral Shah: Parallel computing with graphs and matrices.

• Wed Oct 17: Sparse matrices, graphs, and PageRank. [slides; class diary; annotated diary of the whole PageRank computation (you will need to put the file ucsbweb2007.mat in your home directory)]

• Mon Oct 22: Error and residual, norm and condition number. [diary]

• Wed Oct 24: Floating-point arithmetic. [diary]

• Mon Oct 29: Wrapup of floating-point, error analysis for LU. [diary]

• Wed Oct 31: Least squares and curve fitting. [diary; censusdata.mat]

• Mon Nov 5: Midterm.

• Wed Nov 7: Least squares and curve fitting. [diary; censusdata.mat]

• Mon Nov 12: (Veteran's Day, no class.)

• Wed Nov 14: Orthogonal matrices and QR factorization. [diary; randq.m]

• Mon Nov 19: Guest speaker, Viral Shah: HPC Challenge

• Wed Nov 21: ODEs.

• Mon Nov 26: ODEs: Standard form, Lotka-Volterra equations. [diary; f.m; lotka.m]

• Wed Nov 28: ODEs: Forward Euler and BS23 algorithms. [diary; weightf.m; ode1.m]

• Mon Dec 3: ODEs: Stiff problems. [diary]

• Wed Dec 5: All questions answered.

• Wed Dec 12: Final exam, 12:00 to 3:00 pm.

Other things: