Most materials will be here at
http://www.math.buffalo.edu/~hassard/438-538/
As the term goes on, progressively more material will appear.
Most materials will be here at
http://www.math.buffalo.edu/~hassard/438-538/
As the term goes on, progressively more material will appear.
Classes are Tuesday-Thursday, 2:00-3:20 in Baldy 200-G.
The first class is Tuesday, January 17.
Recitations Thursday, January 26
and will be Thursdays, 8:00-8:50 in Math 250.
Course syllabus/First week handout 438-538_sp12_week1handout.html
The material in 438-538 depends moderately on the material in 437-537.
In Ch. 13, the optimization methods presented are compared with methods for
root finding (Ch. 2). Familiarity with
bisection
and with
Newton's method
for a function of a single variable is assumed.
Also in Ch. 13, familiarity with
Newton's method for systems (
in Rn)
will be assumed. Students should also read
Section 2.6 on the Conjugate gradient method, and review Sections 4.1
and 4.4 on least squares; see also
on
nonlinear least squares
In Ch. 9, numerical methods for stochastic ODE's
expect familiarity with
Euler's method (Ch. 6) and
with the
order of a method for solution of ODE's.
In Ch. 7, derivatives of functions of a single variable are approximated using
finite difference methods, see
two and three point stencil
formulas as in Ch. 5, section 1.
In Ch. 8, derivatives of functions of two variables are approximated using
finite difference methods, see also
five point stencil formulas.
Also in Ch. 8, the finite element method uses a
finite element basis,
in which a collection of continuous functions serves as a basis.
Familiarity with the vector space of continuous functions on a closed interval [a,b]
is assumed.
Stability analysis for both the finite difference and finite methods assume familiarity with
eigenvalues and eigenvectors
for real matrices.
Computer problems in the homework, and the project, will use the
programming enviroment Python/Numpy. This software is freely available.
Installation instructions for Linux, MacOSX and Win64 are given at
http://orange.math.buffalo.edu/~ringland/337/
For Win32, see Win32 installation
Java-based web applets used during the course may
be viewed with firefox on ubuntu after installing
openjdk-6-jre,
icedtea6-plugin.
See Optimization and Random Numbers
See Trigonometric Interpolation and the FFT, Two Dimensional Discrete Cosine Transform and Image Compression and Eigenvalues and Singular Values
Homework assignments,
Homework 1 solutions,
Homework 2 solutions
Homework 3 solutions,
Homework 4 solutions,
Homework 5 solutions
See
Sauer programs in python
for Python/Numpy codes that can be used to work computer homework problems.