MAT 226A - Numerical Methods: Fundamentals
(CRN 43422)
Fall 2009
News
-
November 21:
Solutions to Homework 1 were posted.
-
November 20:
A corrected version of Homework 4
was posted.
-
November 19:
Homework 4 was posted.
The Matlab files g7.m and
k15.m contain the nodes (corresponding to
the integration range [-1,1]) and the weights of the Gauss rule
G_7 and the Gauss-Kronrod rule K_15, respectively.
-
November 4:
One more make-up lecture is schdeuled as
follows:
- Monday, November 23, 4:10 -- 5:00 pm, in MSB 2112
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, 140 Physics-Geology Building
Instructor
-
Roland W. Freund
-
Office: 2140 Mathematical Sciences Building
-
Office Hours: Monday 1:00-2:30 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.
Homework problems
There will be five theory and computational homework sets.
-
Homework 1, due Wednesday, October 14:
pdf file of Homework 1
Solutions to Problems 1-6 of
Homework 1
Numerical results for Problem 7(a) of
Homework 1
Numerical results for Problem 7(b) of
Homework 1
-
Homework 2, due Friday, October 30:
pdf file 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 Friday, November 13:
pdf file of Homework 3
-
Homework 4, due Wednesday, November 25:
pdf file of Homework 4
The Matlab files g7.m and
k15.m contain the nodes (corresponding to
the integration range [-1,1]) and the weights of the Gauss rule
G_7 and the Gauss-Kronrod rule K_15, respectively.
-
Homework 5, due Friday, December 4:
Final exam
There will be a final exam (in class), scheduled as follows:
- Final: Thursday, December 10, 10:30 am - 12:30 pm (Exam Code Q)
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
Information about the Math computing environment is available at the MathComputing Homepage.
You are also encouraged to come and talk with the TA when encountering difficulties.
If you decide to use Matlab as your programming language and need help
getting started, there are many good Matlab tutorials, such as
this one,
available on the web.