18.03 Information

 Spring 1998

(A copy of this information in pdf format is available here, and in postscript here.)

Lectures: Monday, Wedesnday, Friday at 1:00 in 54-100 and at 2:00 in 10-250. Professor Haynes Miller (2-237, 3-7569, hrm@math.mit.edu). Office Hours: variable; announced in lecture and on my home page. This Friday (Feb. 5) they will be 3-5.

Texts: Edwards and Penney, Elementary Differential Equations with Boundary Value Problems, Third Edition; Polking, Ordinary Differential Equations using Matlab (bundled with Edwards and Penney at the Coop); and 18.03 Notes, Problems, and Solutions, sold by Graphic Arts in the basement of Building 11.

Recitations: These small groups will meet twice a week, on Tuesday and Thursday, to discuss the course material. Go to the section to which you have been assigned. If you need to change sections, you must do this through the Undergraduate Mathematics Office (the UMO), 2-108. Your recitation leader is your first line of defense against confusion. Ask questions early and often. A large part of this course is vocabulary, and you must talk about it to understand it. Your recitation leader will also hold office hours, a resource you should not overlook. Another resource of great value is the

Tutoring Room: Monday - Thursday, 3:00-5:00 and 7:30-9:30 PM, Room 2-102. This is staffed by experienced undergraduates. Extra staff is added before hour exams. This is a good place to go to work on homework.

Grading:

Homework: Assignments (except for PS1) will be due on Fridays, by 1:00, in the appropriate box in the doorway at 2-106, next door to the UMO. Each homework assignment will have two parts: a first part drawn from the book or notes, and a second part consisting of problems which will be handed out. The first part will be checked over only briefly, and will contribute less than one-third of the grade on the problem set. The second part will be graded with care, and solutions will be available in the UMO and on the Web on Friday afternoon. Both parts will be keyed closely to the lectures, and you should form the habit of doing the relevant problems after each lecture and not try to do the whole set on Thursday night. Your recitation leader should have the graded problems sets available for you at the next recitation.

I have a strict policy on joint work on homework: I encourage it. But if you do your homework assignments in a group, please write on your solution sheet the names of the students you worked with.

Hour Exams: Hour exams will be held during the lecture hour, on the following three Wednesdays: February 17, March 17, and April 21. Each lecture will be split between two examination rooms, which will be announced in lecture and on the web. If you must miss an exam, go to the UMO before the exam to arrange for a make-up which can be granted under certain limited circumstances such as illness or family emergency.

Final Exam: There will be a three hour comprehensive examination.

Matlab: An important component of this course will be the use of the computer program Matlab. This is standard Athena courseware. A couple of special Matlab packages accompany the book by Pollock and are incorporated into the Athena installation of Matlab.

Home page: Here you will find a variety of information about this course, including this syllabus, office hours, problem sets, solutions, practice exams, occasional handouts, and Professor Miller's own ideas of what he said or at least what he wanted to say in lecture.

Partial Syllabus

This partial syllabus will only be updated sporadically. For a more up-to-date (and complete and correct) syllabus, see the problem sets available from the problem set page.


I. First-order Differential Equations
W 3 Feb Class 1 Separable equations: EP 1.1, 1.4
F 5 Feb Class 2 Direction fields and solutions: EP 1.3, Notes G.1-2; Matlab: Polking 1-14
M 8 Feb Class 3 Linear first order equations: EP 1.5
W 10 Feb Class 4 Applications and substitutions: EP 1.6
F 12 Feb Class 5 Autonomous equations; the phase line: EP 1.8, 7.1
T 16 Feb Class 6 Hour Exam review
W 17 Feb Class 7 Hour Exam I
F 19 Feb Class 8 Numerical methods: EP 6.1, 6.3, Notes G.3; Polking's chapter 5 is optional
II. Second order linear equations
M 22 Feb Class 9 Second order linear equations: EP 2.1, 2.2.
W 24 Feb Class 10 Complex numbers: Notes C
F 26 Feb Class 11 Complex-valued functions; the case of real roots: EP 2.3.
M 1 Mar Class 12 Non-real and repeated roots: EP 2.3, 2.4.
W 3 Mar Class 13 Initial value problems, Wronskian, operators: Notes O 4-8.
F 5 Mar Class 14 Operators: Notes O, handout.
M 8 Mar Class 15 Undetermined coefficients, resonance: EP 2.5, handout.
W 10 Mar Class 16 Applications.
F 12 Mar Class 17 Linear equations with nonconstant coefficients: EP 2.6.
M 15 Mar Class 18 Review.
W 17 Mar Class 19 Hour Exam II
F 19 Mar Class 20 Eigenvalue problems: EP 2.10; Airy functions handout.
III. Systems of First Order ODEs
M 29 Mar Class 21 Elimination and the opposite: EP 5.1 (355-359).
W 31 Mar Class 22 Eigenvalues: Notes LS 1.1, 1.2.
F 2 Apr Class 23 Complex or repeated eigenvalues: Notes LS 1.3, 1.4.
M 5 Apr Class 24 Initial value problems: Notes LS 2.1-2.3.
W 7 Apr Class 25 Dynamics of linear systems: Notes GS 1-5.
F 9 Apr Class 26 Dynamics of nonlinear systems; linearization: Notes GS 6-7, Handout.
M 12 Apr Class 27 Example: The nonlinear pendulum: 7.5 (556--558, 561).
W 14 Apr Class 28 Matrix exponentials: EP 5.7 (441-443).
F 16 Apr Class 29 Spinning books -- a review; Handout.
W 21 Apr Class 30 Hour Exam III
IV. The Laplace Transform
F 23 Apr Class 31 Basic properties: EP4.1.
M 26 Apr Class 32 Solution of IVPs: EP 4.2 (302-306), 4.3.
W 28 Apr Class 33 Discontinuous functions: EP 4.5 (328-333).
F 30 Apr Class 34 Convolution and the delta function: EP 4.4 (320-322), 4.6 (341-348).
M 3 May Class 35 Transfer functions and Duhamel's principle: Notes LT, EP 4.6 (349-350).
V. Fourier Series and Partial Differential Equations
W 5 May Class 36 Fourier Series: EP 8.1.
F 7 May Class 37 Periodic solutions of ODEs: EP 8.3, 8.4.
M 10 May Class 38 Heat Equation: EP 8.5.
W 12 May Class 39 Course review.