**RUTGERS UNIVERSITY -- NEW BRUNSWICK
**

**DEPARTMENT OF MATHEMATICS **

**MATHEMATICS 252:01 HOME PAGE -- SPRING
2000**

**"Mutationem motus
proportionalem esse vi motrici impressae, et fieri secundum lineam rectam
qua vis illa imprimitur." **(Newton's Second Law of Motion,
**F** = d/dt[m**v***].)*

*Isaac Newton
(1642--1727)*

- Textbook:
- Required: P. Blanchard, R. L. Devaney
& G. R. Hall,
*Differential Equations*, Brooks/Cole (1997), ISBN# 0-534-34550-6. - Rutgers University Academic Integrity Policy
- Inst.: Bertram Walsh, Hill 728, (732) [44]5-3733; e-mail bwalsh@math.rutgers.edu.
- Office hours:
- Hill 728 (Busch) Th4 & F3
- (and by appointment at any mutually convenient time)
- NB: Note that the regular hours have changed as a result of reassignment of the instructor.
- Course Materials: (most linked names will be .pdf files)
- (Current) Section Syllabus
- Link(s) to earlier versions of various Class Notes
- Note set N1 (modeling)
- Note set N2 (bifurcation)
- Maple Lab 1 distributed 1/27/2000, in .pdf format
- §1.3 Problems in a Maple session (.pdf format, with thanks to Professor Bumby)
- A set of notes on Euler's method, again in .pdf format, new for Spring 2000.
- A set of notes on linearization of material in the first few §§ of Ch. 2, in .pdf format.
- An exact determination of the trajectories for the rabbits-and-foxes equations in the first few §§ of Ch. 2, in .pdf format.
- Note set N3 (phase plane notes, in .pdf format).
**Sample****First Hour Exam**(from Spring 1999), in .pdf format.- A solved copy of this year's first hour exam, in .pdf format.
- A set of notes on matrix exponentials in .pdf format, the notes N4 of the syllabus.
- 7 pp. of notes on first-order linear systems, giving a real matrix approach to 2-by-2 systems with
complex eigenvalues. You may (or may not) find this approach more
congenial than passing to complex exponentials immediately. It is
**not examination material**. In any event, it would be good to read it before reading the material on*n*-by-*n*skew-symmetric systems linked below, if you should find the latter material interesting. - 9 pp. of notes on first-order linear systems with skew-symmetric coefficient matrix; this is
**not examination material**, but will be useful to serious students of physics and mechanical engineering. - A set of notes on 1st order linear homogeneous systems in .pdf format, prepared for Math 250 but others may be interested. These contain a proof of the uniqueness theorem for those systems.
- 9 pp. of notes summarizing coördinates and matrices in .pdf format, deriving useful material about change of basis (see particularly §3).
- A 3-pp. summary in .pdf format of the notes above. (Already circulated in class.)
- Minutes of the 3/30/2000 class working out a detailed example of a 2-by-2 system in which the matrix of coeffcients has only one eigenvalue (the phase-plane system of a critically damped harmonic oscillator); this is also relevant to the material of Ch. 4.
**Sample****Second Hour Exam**from Spring 1999, in .pdf format.- A solved copy of this year's second hour exam, in .pdf format.
- A laundry list of things to review for the 2nd
hour exam, copied
*verbatim*from the Spring 1999 version of this course, with no guarantees that it is entirely relevant this year. - A laundry list of things to review for the final
exam, copied
*verbatim*from the Spring 1999 version of this course, with**no guarantees**that it is entirely relevant this year. - Notes on Variation of Parameters for 1st-order inhomogeneous systems and 2nd-order inhomogeneous equations with constant coefficients.
**A sample****Final Exam**from a previous year, in .pdf format. This version (as of 1050 EDT, 5/2/2000) now contains solutions. Peace to Mr Greenfield. There are**no guarantees**that this year's final will resemble it, except that the level at which the material is tested will be no more difficult.

- Examination Announcements and Materials:
- First Hour Exam: March 6th; link to results
- Second Hour Exam: April 17th; link to results
- Final Examination: May 11th 0800--1100 EDT SERC-212
- Please submit your
`Maple`work no later than the final exam. - Important announcement about Makeup Examinations

The .pdf files listed above are set in small type whose legibility on some terminals may be marginal. You're almost surely using an Acrobat reader to read these files: clicking on a magnification icon and selecting "fit visible" may improve things. You may find that the best solution for the legibility problem is to produce hard copies (or to obtain them from the instructor if you are unable to produce them yourself).

GRADING GUIDELINES: While this is not graven in stone, department practice for Calculus I-IV has been to grade on a 450 point scale with 100 points for each hour exam, 200 points for the final, and 50 points distributed over quizzes and problem sheets. The percentages are thus approximately 22+22+44+11. I plan to stick with this except for one caveat: if the 252 instructors as a group want to weight the projects more heavily, say percentages 20+20+40+20, then I will move in that direction if I have majority student consent. In all cases I expect to delete the lowest two quiz scores.

last revised 1508 EDT 05/12/2000