A Short Course on Approximation Theory
Please read the
disclaimer and description
before downloading these notes.
This is a set of lecture notes for a short course on Approximation
Theory that I have offered several times to graduate students at
Bowling Green State
University, Bowling Green, Ohio. In its first few
incarnations, I used T. J. Rivlin's
An Introduction to the Approximation of Functions,
Dover, 1981, as a supplementary text. In recent years, I've
tried to make the notes self-contained, although there
are still plenty of references to Rivlin (and other texts).
The course is intended as a survey of elementary techniques in
Approximation Theory for novices and
non-experts. Experts in the field seeking
new, original, or research topics should look elsewhere.
This is strictly for beginners!
Prerequisites for a thorough understanding
of the course include:
- A first course in advanced calculus or real analysis
(pointwise and uniform convergence, compactness, etc.).
- A rudimentary knowledge of normed spaces and completeness.
- A course in linear algebra.
There is enough material here for roughly 25 hour-and-a-half
lectures; probably not quite enough for a full semester course.
On the other hand, it is sufficient background to facilitate reading
more advanced books on the subject. I should also point out
that the choice of topics reflect my personal interests and
I make no claims that they will suit everyone's tastes.
The notes are available here in
pdf format.
The file is roughly 784Kb and the printed version is 159 pages.
Neal Carothers -
carother@bgnet.bgsu.edu