RUTGERS UNIVERSITY -- NEW BRUNSWICK
DEPARTMENT OF MATHEMATICS
MATHEMATICS 642:573 HOME PAGE -- FALL 2000
"Round numbers are always false."
Samuel Johnson,
LL.D. (1709--1784), in Boswell's Life of Johnson, Mar. 30
1778.
- Textbook:
- (Required) Text: Kendall E. Atkinson, An Introduction to Numerical Analysis, 2nd ed., Wiley (1989) ISBN# 0-471-62489-6.
- Rutgers University Academic Integrity Policy
- Instructor:
- Lecturer: Bertram Walsh, Hill 728, (732) [44]5-3733, bwalsh@math.rutgers.edu
- Office hours:
- Monday 5th (2:50--4:10) at Hill 728 (Busch), 'phone (732) [44]5-3733
- Thursday 2nd (9:50--11:10) at Chem 207A (Douglass), 'phone (732) [93]2-9378
- Appointments at mutually agreed & convenient times/places.
- Prerequisites:
- (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 equations.
- Tentative course syllabus.
- References: A short bibliography in .html format.
- Course Materials:
- 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 Geršgorin's theorem) will be useful to have this semester.
- 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. (10/07/2000).
- 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 elimination.
- 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 still coming.
- Sets of Exercises:
- Exercise Set 1.
- Exercise Set 2.
- Exercise Set 3.
- Midterm problem set due 11/6/2000.
- Exercise Set 4.
- Exercise Set 5.
- 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]
- A previous syllabus for 642:573;
- A list of Web resources for numerical analysis.
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