Numerical analysis
MAD6407-3135
Spring 2004
- Instructor
- Jay Gopalakrishnan
- Venue
- Little Hall 223
- Time
- MWF 3:00-3:50pm
- Office hours
-
Tuesdays 3:00-3:50pm or by appointment.
- Prerequisites
-
Undergraduate analysis, and knowledge of a programming language or
MATLAB™. Although MAD6406 is
not a prerequisite, students are recommended to take it before taking
this course.
- References
-
- Textbook: "Numerical Analysis: Mathematics of Scientific
Computing" (3rd edition) by David Kincaid and Ward Cheney, 2002.
- Additional reference: "Introduction to Numerical Analysis", by
J. Stoer and R. Bulirsch, 1992.
- Additional reference: "An introduction to numerical analysis", by
Kendall Atkinson, 1988.
- Course objective
-
This course introduces concepts in the development and analysis of
algorithms often needed to solve mathematical problems. (Study of
algorithms in numerical linear algebra is not part of this course as
it is the subject of
MAD6406.)
- Course outline
-
- Core topics
- Nonlinear equations and systems.
-
(Bisection, Newton-Raphson iteration, generalization to systems,
secant method,
fixed point iterations, polynomial rootfinding,
methods based on homotopy)
- Approximating functions.
-
(Lagrange and Hermite interpolation, spline interpolation, cubic
splines, B-splines,
best approximations in innerproduct spaces,
Chebyshev theory of best approximations,
Trigonometric interpolation, Fast Fourier Transform.)
- Numerical differentiation and integration.
-
(Divided differences, Richardson extrapolation,
trapezoidal and Simpson rules,
Newton-Cotes formulae, Peano kernels, orthogonal
polynomials, Gaussian quadrature, Romberg integration)
- Numerical solution of ordinary differential equations.
-
(consistency and stability, Runge-Kutta methods, Adams methods,
predictor-corrector scheme,
stability of multistep schemes, boundary value problems.)
- Further topics
- Stiff problems
- More on B-splines
- Galerkin methods
- Evaluation
-
Computational assignments will determine 20% of your total grades. The
remaining component of your grades will be determined by examinations
as follows:
- Two midterm examinations (20% each)
- Final examination (40%)
Exercises will be given on a regular basis during the lectures (no
formal handouts will be given). You are not required to turn in
solutions.
- Mailing list
- s04-3135@clas.ufl.edu
This mailing list provides a forum for everyone to communicate to
entire class, raise questions on assignments, publicize typos,
advertise seminars or talks of interest to class etc.
Please sign up for this mailing list by sending email to
s04-3135-request@clas.ufl.edu (not s04-3135@clas.ufl.edu)
with the single word "subscribe"
(without quotes) as the message body (not subject). When you get a
reply, follow further instructions in it.
- Additional information
-
- Policy related to make-up exams or other work: There will
be no opportunities to make up for work not submitted. However, if a
student provides a legitimate excuse well in advance, scores will be
prorated. Work with due date should be turned in at the beginning of
class on the stated due date. Late work will not be accepted
and will be deemed work not submitted.
- Policy on class attendance: Class attendance is not mandatory.
- University's honesty policy: All students are expected to
know and abide by the University of Florida Honor Code. E.g., on all
work submitted for credit by University of Florida students, the
following pledge is either required or implied: "On my honor, I have
neither given nor received unauthorized aid in doing this
assignment." Know your responsibilities (and rights) as detailed in
Student Guide.
- Copyrighted materials: All course materials handed out in
class or placed on the web are protected by copyright laws, and are
for personal use only. Multiple copies or sale of these materials is
prohibited.
- Students with disabilities: Students requesting
classroom accommodation must first register with the Dean of Students
Office. The Dean of Students Office will provide documentation to the
student who must then provide this documentation to me
when requesting accommodation.
Jay Gopalakrishnan
March 19, 2004