MAT 226A - Numerical Methods: Fundamentals
(CRN 83862)
Fall 2011
News
-
December 13:
The posted numerical results for Problem 5(d) of
Homework 4 were incorrect;
the numerical results are correct now.
-
December 11:
Here are (quite detailed)
solutions to the problems
on the final exam.
-
December 5:
Solutions to Homework 5 were posted.
Description
Fundamental principles and methods in numerical analysis, including the
concepts of stability of algorithms and conditioning of numerical
problems, numerical methods for interpolation and integration, eigenvalue
problems, singular value decomposition and its applications.
Outline of major topics:
- Two Examples of Numerical Methods
- LU factorization
- Newton's method
- General Principles
- Conditioning
- Floating-point arithmetic
- Stability of algorithms
- Interpolation
- Integration
- Gaussian integration
- Adaptive integration
- Eigenvalue problems
- Singular Value Decomposition
- Bidiagonalization
- QR decomposition
- Least-squares problem
- Ill-posed problems
- Generalizations of SVD
Lectures
-
MWF 11:00-11:50 am, Physics 140
Instructor
-
Roland W. Freund
-
Office: 2140 Mathematical Sciences Building
-
Office Hours: Monday 12:30 - 2:30 pm
No required textbook. Optional references:
-
G. Dahlquist and A. Bjoerck. Numerical Methods.
Dover Publications, 2003.
-
G. Dahlquist and A. Bjoerck. Numerical Methods in
Scientific Computing, Volume I.
SIAM, 2008.
-
L.N. Trefethen and D. Bau, III.
Numerical Linear Algebra.
SIAM, 1997.
-
C.B. Moler. Numerical Computing With Matlab.
SIAM, 2004.
Prerequisites
Working knowledge of MATLAB is expected.
If you do not know or remember how to use MATLAB, please follow
one of the self-study guides for MATLAB listed below.
Homework problems
There will be five theory and computational homework sets.
You are required to use MATLAB to complete the computational parts of
the homework sets.
-
Homework 1, due Wednesday, October 12:
pdf file of Homework 1
Matrix A for Problem 3(f)
Solutions to Problems 1-5 of
Homework 1
Numerical results for Problem 3(e) of
Homework 1
Numerical results for Problem 3(f) of
Homework 1
Numerical results for Problem 6(a) of
Homework 1
Numerical results for Problem 6(b) of
Homework 1
Numerical results for Problem 6(c) of
Homework 1
-
Homework 2, due Wednesday, October 26:
pdf file of Homework 2
Solutions to Problems 2-6 of
Homework 2
Numerical results for Problem 1(a) of
Homework 2
Numerical results for Problem 1(b) of
Homework 2
Numerical results for Problem 1(c) of
Homework 2
-
Homework 3, due Wednesday, November 9:
pdf file of Homework 3
Solutions to Problems 1-7(c) of
Homework 3
Numerical results for Problem 7(d) of
Homework 3
Numerical results for Problem 8 of
Homework 3
-
Homework 4, due Wednesday, November 23:
pdf file of Homework 4
Solutions to Problems 1-3 and 5 of
Homework 4
Plot for Problem 4(c) of Homework 4
Numerical results for Problem 4(c) of
Homework 4
Plot for Problem 4(d) of Homework 4
Numerical results for Problem 4(d) of
Homework 4
Numerical results for Problem 5(d) of
Homework 4
-
Homework 5, due Friday, December 2:
pdf file of Homework 5
Solutions to Problems 3-5 of
Homework 5
Numerical results for Problem 1(c) of
Homework 5
Numerical results for Problem 2(b) of
Homework 5
Final exam
There will be a final exam (in class), scheduled as follows:
- Final: Friday, December 9, 6:00 - 8:00 pm (Exam Code Y),
in Physics 140
Grading percentages
- Homework: 50%
- Final exam: 50%
Computer accounts
You can get an account on the Mathematics Department
system by going to
http://www.math.ucdavis.edu/comp/class-accts
If you wish you should be able to use your account remotely by using some form of s
ecure
shell (e.g., ssh under unix/linux or PuTTY on non-unix
systems) to
connect to point.math.ucdavis.edu. It may be helpful to invoke MATLAB
with the command matlab -nosplash -nojvm, which will make it
run in your terminal window.
Information about the Math computing environment is available at the
MathComputing Homepage.
Matlab resources
A MATLAB Primer (second edition) can be found
here;
a list of some MATLAB tutorials is available
here.
There is also an online version of the book by
Numerical Computing with MATLAB
by Cleve Moler.
For more details, the official MATLAB manual
is available from MATLAB Online Help Desk (for web) and MATLAB Online Manuals
(in PDF).
You may find additional useful information by searching online with your
favorite search engine.
Dates
-
Academic Holidays: November 11, November 24-25
-
Last day of instruction for this class: Friday, December 2