RUTGERS UNIVERSITY -- NEW BRUNSWICK
DEPARTMENT OF MATHEMATICS
MATHEMATICS 642:573 HOME PAGE -- FALL 2000
"Round numbers are always
Lecturer: Bertram Walsh, Hill 728, (732) 5-3733,
Monday 5th (2:50--4:10) at Hill 728 (Busch), 'phone (732) 5-3733
Thursday 2nd (9:50--11:10) at Chem 207A (Douglass), 'phone (732) 2-9378
Appointments at mutually agreed & convenient times/places.
(Undergraduate) advanced calculus, linear algebra, and differential equations.
This course is suitable for graduate students in the exact sciences and
for engineering graduate students. Advanced undergraduates who have
the prerequisites are welcome to explore with the instructor the possibility
of their taking this course.
Course description: (inc. 2nd semester)
Ideas and techniques of numerical analysis illustrated by problems in the
approximation of functions, the numerical solution of linear and nonlinear
systems of equations, the approximation of matrix eigenvalues and eigenvectors,
numerical quadrature, and the numerical solution of ordinary differential
Tentative course syllabus.
References: A short bibliography
in .html format.
Sets of Exercises:
A first set of notes on difference equations and
inequalities, sources of error in floating-point calculations, and
the like, in .pdf format.
A first set of notes on computational linear algebra,
in .pdf format. These were prepared for Math 642:574 in Spring 2000, but
some of the material (like Gergorin's theorem) will be useful to have
Notes on polynomial interpolation in the usual
.pdf format. These notes are complete (9/23/2000).¹
Two little lemmas on weighted averages that
are frequently handy for estimating errors.
- A resumé of polynomial
interpolation prepared for an earlier incarnation of 573, but
still perhaps useful (in .pdf format); references to Atkinson have
been updated to the second edition. Some overlap with #3 above will
be noted (and cannibalization obvious).
- Notes on rootfinding in the usual .pdf
format. 32 pages are present (10/2/2000) and a few more will come,
but they're not quite in final form (10/3/2000).
- Notes on polynomial
approximation in .pdf format.² Complete at 39 pp.
- Notes on approximation & interpolation
by trig functions, finitized Fourier transforms, and related
matters, in .pdf format. Complete at 33 pp. (10/18/2000).³
- Notes on spline interpolation, in .pdf
format. Complete at 24 pp. (10/26/2000). Many typos were
corrected in this last post; you may want to make a fair copy.
- A brief discussion of diagonally
dominant matrices and why they behave so well under Gaussian
- Notes on Gaussian quadrature, in .pdf
format. 5 pp. (10/28/2000).
- Notes on the Euler-Maclaurin sum
formula and asymptotic error formula for composite trapezoidal
quadrature, in .pdf format. 11 pp. (10/30/2000).
- Notes on adaptive quadrature, in .pdf
format. 4 pp. (11/06/2000).
- Notes on the initial-value problem for ordinary
differential equations, in .pdf format. 26 pp. (11/20/2000) with
more to follow.
- More linear algebra, including the
Perron-Frobenius theorem and Gauss-Jacobi vs. Gauss-Seidel iterative
solution schemes, in .pdf format. 10 pp. (12/11/2000) with a bit more
Course Materials from Previous Incarnations of 573:
[NB: These don't belong to the lecturer and may be moved, causing links
to fail, but they'll be restored]
- Exercise Set 1.
- Exercise Set 2.
- Exercise Set 3.
- Midterm problem set due 11/6/2000.
- Exercise Set 4.
- Exercise Set 5.
¹Not as much was wrong with p. 17 as I had thought; only
the inequality at the bottom of the page needed to be changed to the
strict inequality i < j.
²I had thought to put trigonometric and polynomial
approximation/interpolation together in one set, but the set just kept
getting longer; so the notes on trig/complex-exponential matters will
be separate. (Added 0648 EDT 10/09: there are small typos on pp. 37
and 39. I will list them in class, but you might just want to print
pp. 37-39 from the corrected version.)
³One or two easily spotted typos from previous posts were
repaired, but p. 30 was somewhat rewritten: you may want to make a
fair copy from p. 29 ff.
Last revised 0742 EST 12/11/2000