Robert Indik
email:
indik@math.arizona.edu
(most reliable contact method)
telephone: 621-4599, office
location: Math East 249A
Office Hours (subject to change): Monday
at 10AM and Friday at 3PM in Math east 249a, Thursday 2PM in math 202
(U.D. tutoring)
Please subscribe to the MATH575 mailing list/list server. This should be a convenient forum for questions on material and homework. The name of the list is "MATH575" follow this link to get instructions for subscribing. Solutions and grades will be posted using the university of Arizona D2L server.
You may want to buy these directly from SIAM, if you accept the
free student
membership in SIAM (Society for Industrial and Applied Mathematics)
that you can get as a student at an affiliated University, the
discount for the books is significant. It is also a great
organization.
Click on the links below to go to the publisher's
website.
Numerical
Linear Algebra by Trefethen and Bau, SIAM Press
We will
be using this text for the first 8-9 weeks of the semester. The
first 5 lectures in the book are available online at
http://www.comlab.ox.ac.uk/nick.trefethen/text.html
We
have used
Computer
Methods for Ordinary Differential Equations and
Differential-Algebraic Equations by Uri M. Ascher and Linda R.
Petzold, SIAM Press
in the past, and most likely will this
year as well starting near the end of this semester and for 575b-- a
definite decision will be made shortly.
We will also
make some use of the online notes
that Prof. Restrepo created.
We will have a midterm and a final, and (mostly) weekly homework
assignments. In the second half of the semester we will be
using MATLAB quite heavily, and those homework assignments can be
completed either as printed output, or as posted web pages.
Homework will be assigned each class, and will be due before 4PM the
Tuesday following the class during which it is assigned. I will try
to keep this web page up to date with homework assignments.
Homework counts as 50% of the grade, the midterm as 20% and the final
as 30%.
You will need to have access to a computer where you
can run MATLAB. Students in the Math department can access
MATLAB on the departmental Linux machines. All university
students are entitled to accounts on the u.arizona.edu cluster, and
can run MATLAB remotely on that cluster. In addition, the MS
Windows machines in the Info commons also have a limited number of
MATLAB licenses which should be accessible from all of the stations.
If you have your own computer, you can take advantage of the Matlab
site license, and install the software. Please see the instructions
at https://sitelicense.arizona.edu/matlab/index.php
.
Students entering this class are expected to have a solid background in Linear Algebra, in Calculus and Ordinary Differential Equations. It is quite helpful to have some computer programming experience, especially in MATLAB.
We will have a single midterm exam and a final exam. Our final is scheduled for Tuesday December 16th 11-1 in Math 501. Our midterm is scheduled for Tuesday October 28th during the regular class meeting.
HW1, Due Tuesday September 2:
Lecture 1: 1.1, 1.3, 1.4
Lecture 2: 2.1,
2.3, 2.4, 2.6
HW2, Due Tuesday September 9:
Lecture 3:
3.2 3.4 3.5
Lecture 4: 4.1 4.4 4.5
Matlab introduction: Do part I only of
the homework assignment found by following this
link
HW3 Due Tuesday September 16:
Lecture 5: 5.2,
5.3, 5.4
Lecture 6: 6.1, 6.2, 6.3
HW4 Due Tuesday
September 23:
Lecture 7: 7.1 7.3 7.5
Lecture 8:
8.2, 8.3 + implement and test the CGS algorithm (Alg. 7.1) and
compare its results to those of Alg. 8.1
Matlab work must include listings of your
functions, as well as some evidence of your tests of the programs and
discussion of the errors.
HW5 Due Tuesday September 30:
Lecture 9: 9.1, 9.2
and use your
programs for Algorithm 7.1 and Algorithm 8.1 to duplicate
experiments 2 and 3 from Lecture 9. Produce a plot Like figure
9.1 and discuss the meaning of the results you compute.
Lecture 10: 10.1, 10.2, 10.4
HW6 Due Tuesday October 7:
Lecture 11: 11.1 11.2 11.3
Lecture 12: 12.1
12.2 12.3
HW7 Due Thursday October 16:
Lecture 13: 13.1 13.2 13.3
Lecture 14:
14.1 14.2
HW8 Due Thursday October 23:
Lecture 15: 15.1 abcd only 15.2 ab (not c)
Lecture 16: 16.1, 16.2
HW9 Due Thursday
October 30:
Implement and test Algorithm
17.1 (use random triangular matrices to test and verify that the
algorithm is producing results that are as accurate as the theorems
predict.)
HW10 Due Tuesday Nov 4
Lecture 18:
18.1, 18.2
HW11 Due Thursday Nov 13
Lecture
19: 19.1, 19.2
Lecture 20: 20.1, 20.2
Lecture 21: 21.2, 21.6
HW12 Due Thursday Nov 20
Lecture 22: 22.1, 22.3
Lecture 24: 24.3,
24.4
Lecture 25: 25.1
HW13 Due Tuesday Dec
2
Click here for the
assignment
HW14 Due Tuesday Dec 9
Problems from Ascher+Petzold book
Chapter 2: 2.3,
2.4
Chapter 3: 3.2, 3.4
Below is a syllabus for the first
semester.
Part I: Numerical Linear Algebra (following
Trefethen and Bau):
Review of Linear Algebra
Fundamentals:
Matrix
Vector Multiplication
Orthogonal Vectors and Matrices
Norms
The
Singular Value Decomposition
QR Factorization and Least Squares
Projectors
QR
Factorization
Gram-Schmidt Orthogonalization
Householder
Triangularization
Least Squares Problems
Conditioning and Stability
Conditioning and
Condition Numbers
Floating Point Arithmetic
Stability
Stability
of Householder Triangularization
Stability of Back
Substitution
Conditioning of Least Squares Problems
Stability
of Least Squares Algorithms
Systems of Equations
Gaussian
Elimination
Pivoting
Eigenvalues
Eigenvalue
problems
Overview of Eigenvalue Algorithms
Iterative Methods
Overview of Iterative Methods
Part II: Computer Methods for
Ordinary Differential Equations (following Ascher and
Petzold)
Background in ODEs
Initial Value Problems
Problem stability
Basic Methods and Stiffness
Forward
Euler
Convergence, Accuracy, Consistency and 0-Stability
Absolute
stability
Stiffness and Backward Euler
A-stability
Trapezoid
method