# AMSC 460 / CMSC 460 Computational Methods Section 0101

## Information for Fall 2007

Dianne P. O'Leary

December 11:
Extra office hours on December 11: After class, until 1pm, and
3--4pm.

oleary@cs.umd.edu

** When and Where: **
TuTh......11:00am-12:15pm (CSI 1121)

** Office Hours: **
Monday 1:15-3:15pm, Thursday 8-9am,
and by appointment,
in AVW 3271.

Email welcome anytime.
My other course meets TTh 9:30 - 10:45.

Interesting
internship opportunity for Summer, 2008

** Textbook:**
Introduction to Scientific Computing, 2nd edition (newest) by
Charles F. van Loan, Prentice Hall.

** Prerequisite:**
Programming, advanced calculus, linear algebra.

** Topics:**
Basic computational methods
for solving problems which arise frequently in the physical,
engineering, and natural sciences. Emphasis on problem
solving methods and their computational aspects.

Course Outline

** Final Exam: **
Thursday, December 13, 8-10am

** Teaching Assistant: ** Sima Taheri

Office hours: Room AVW 1112.
Starting October 6, the schedule will be
Wednesday 11-1; Friday 10-12.
Email: sima.taheri@gmail.com

** Basic Information: **

** Course notes: **
If notes are reposted, then changes are indicated in green type.

** In Class Exercises: **
The purpose is to give you extra time practicing with the techniques
we discuss. You will receive 3-5 points for making an honest effort
to complete the challenge. Perfection is not necessary.
For the first two exercises (while we
get comfortable with the machines), I'll give you the option of
continuing to work on them until the following Monday.
Exercise 1: Challenge 1.4 from the Unit 1 notes. Submit by sliding
a paper under my door or sending me email.
Exercise 2: Use
elephant.m
and elephant.tif
to answer these questions:
Which of the three interpolation methods
works best?
Where do you put the interpolation points
in order to get the best fit to the elephant?
Exercise 3: Solve P2.3.3 in van Loan, but use f(x) = log x rather
than f(x) = e^{ax}.
Exercise 4: October 4.
Finish the exercise and
submit by sliding
a paper under my door or sending me email by midnight October 8.
Exercise 5: October 11.
Finish the exercise and
submit by email by midnight October 15.
Exercise 6: October 18. Program ``forward substitution"
(a) componentwise; (b) by rows; (c) by columns.

Answer: see the three Matlab codes in Section 6.1.1 of van Loan's book.
Exercise 7:
November 1.

Part 1.
For Part 2, run
exlinsys.m
and comment on the results.

A program to solve part 1:
runsunspot.m
Note that there will be a question on part 2
on Tuesday's quiz.
Exercise 8: November 8.

Write your own Matlab program to plot the trajectory
of the
Lorenz attractor in the top figure of the Wikipedia
webpage.

Here is a
Matlab gui to play with.
Exercise 9: November 29.

1. Download fzerogui.m and polyinterp.m from the Mathworks website.
Try fzerogui on three of the functions listed in "help fzerogui"
and comment on the results.

2. Use fsolve.m to solve the system of equations

x^2 + y^2 - 5 = 0,

y - x^2 -1 = 0.
Exercise 10: December 6.

1. Fit a straight line to the data (1,2), (3,4), (7,5), (10,24).
Write the equation for the straight line and give
the norm of the residual.

2. Let the matrix from problem 1 be called A.
Use Matlab's qr command to write an orthonormal basis for
(a) The range of A. (b) The nullspace of A'.
** Homework: **

Homework 1: Due Sept 18
The assignment
hw1.m
Submission instructions
Answers.
Mean= 7.4/10; Median = 7/10.
Homework 2: Due Oct 2
The assignment
Submission instructions: same as Homework 1.
You may use van Loan's software for Hermite cubic interpolation
or Matlab's pchip. (Matlab's pchip is a bit easier -- it doesn't require
you to specify derivative values.)
Answers.
Mean= 8.1/10; Median = 9/10.
Homework 3: Due Oct 16
The assignment
Submission instructions: same as Homework 1.
FAQ
Answers.
Mean= 10.8/15; Median = 10/15.
Homework 4: Due Oct 30
The assignment
Submission instructions: same as Homework 1.
FAQ
Answers.
Homework 5: Due Nov 13
The assignment
Submission instructions: same as Homework 1.
Answers
Homework 6: Due Nov 27
The assignment
Homework 7: Due Dec 11
The assignment
Submission instructions: same as Homework 1.
FAQ
New!
The answers
** Quizzes and Exam: (tentative schedule)**

quiz 1: September 11
questions
and answers.
Mean= -7.7; Median = -6.
quiz 2: September 25
questions
and answers.
Mean= -5; Median = -5.
quiz 3: October 9
questions
and answers.
Mean= -6.6; Median = -5.
quiz 4: October 23
questions
and answers.
Mean= -6.3; Median = -6.
quiz 5: November 6
questions
and answers.
Mean= -6; Median = -5.
quiz 6: November 20
questions
and answers.
Mean = -9; Median = -9.
quiz 7: December 4.
questions
and answers.
Mean = -9; Median = -9.

This quiz covers solution of nonlinear equations.
Be sure you know how to use fzero and fsolve.
Final Exam questions and answers:
New!
questions and answers
Mean = 100; Median = 101.
** Sample Quizzes and Exams: **
quiz 1:
2001 questions
and answers
2002 questions
and answers
quiz 2:
2001 questions
and answers
2002 questions
and answers
quiz 3:
2001 questions
and answers
2002 questions
and answers
quiz 4:
2001 questions
and answers
2002 questions
and answers
quiz 5:
2001 questions
and answers
2002 questions
and answers
quiz 6:
2001 questions
and answers
2002 questions
and answers
quiz 7:
2001 questions
and answers
2002 questions
and answers
quiz 8:
2001 questions
and answers
2002 questions
and answers
quiz 9:
2001 questions
and answers
2002 questions
and answers
Final exams:
2001 questions
and answers
2002 questions and answers
(12/03/2007: Questions and answers are in a single file.)