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:
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 reflects my personal interests and
I make no claims that they will suit everyone's tastes.
- 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.
The notes are available here in
The file is roughly 784Kb and the printed version is 159 pages.
Neal L. Carothers