MIAMI-DADE COLLEGE

KENDALL CAMPUS

MATHEMATICS DEPARTMENT

MAP 2302 INTRODUCTION TO DIFFERENTIAL EQUATIONS Reference #328463

Meeting times: MWF 11:00am–11:50am Meeting place: Room 9119

SYLLABUS AND COURSE OUTLINE SPRING 2006

INSTRUCTOR: Professor Orr

OFFICE Room 3238-2

PHONE 305-237-2013

EMAIL dorr@mdc.edu

WEBPAGE http://faculty.mdc.edu/dorr

OFFICE HOURS MW 9:00am–10:00am

F 12:00pm–3:30pm

TR 9:50am–11:05am and 2:00pm–4:00pm

TEXTBOOK: A First Course in Differential Equations, 8^th Edition, by Dennis G. Zill, Brooks Cole publishers.

PREREQUISITE: MAC 2312 (Calculus with Analytic Geometry II), with a grade of “C” or better.

GRADING:

HOMEWORK Homework will be assigned during each class meeting. The assigned homework problems constitute a list of the things you will be expected to know how to do. The best way to ensure that you know how to do something is to actually do it on a regular basis. Although the homework assignments will not be collected or graded, you must complete these assignments in order to learn the course material and prepare yourself for the exams. Questions appearing on the exams will be similar to those encountered in the homework.

TESTS There will be six unit-tests given throughout the semester, plus a comprehensive final exam. All tests, including the final exam, will carry equal “weight”. In order to be counted, each test must be taken in class at the scheduled time, unless alternate arrangements are made in advance. If you miss a test, a score of zero will be recorded. At the end of the semester, the single lowest score among the six unit-tests will be replaced by the final exam score, provided this works to your advantage. (Note: When the final exam score replaces a lower test score, the result is that the final exam carries double “weight”; it counts once in its own behalf, and once again for the score it replaces.)

FINAL EXAM A comprehensive final exam will be administered during final exam week. The final exam will be mandatory, and will thus determine at least one seventh of the course grade.

GRADES You may exercise your option to drop the class with a “W” grade, provided you initiate such action no later than Wednesday, March 15. (Note: This withdrawal deadline is established through the Registrar's Office and is subject to change. You may wish to contact the Registrar in advance for confirmation of the withdrawal deadline.) If you have not withdrawn from the class by that date, I will be required to assign you a grade at the end of the term. I will calculate the average of your test scores and translate the result into a letter grade. The most stringent grade scale I will enforce is as follows:

A — 90% or better

B — 80%–89%

C — 70%–79%

D — 60%–69%

F — below 60%.

Please note that if you do not sit for the final exam, I reserve the right to assign you an “F” grade regardless of your semester average.

ATTENDANCE: You are expected to attend all class meetings. Furthermore, you are expected to arrive on time and not to leave until class is dismissed. Your grade will not be directly affected by your attendance record, except as noted in the next paragraph. However, if you miss a test, and are then absent from three consecutive class meetings immediately following that missed test, I reserve the right to purge you from my roll by assigning you a “WI” grade. Please note that the previous sentence defines my option—it does not guarantee that that option will be carried out. If you decide that you actually desire a “W” grade, you are responsible for initiating the withdrawal process by March 15. If you simply abandon the class without formally withdrawing, you are just as likely to receive an “F” as a “WI”.

It is also worth noting that a good attendance record can have a positive effect on your final grade in certain borderline cases. This is especially true if your final class average is below 60%. Frequently a student with a low average who has attended class regularly and shown evidence of making a sincere effort may be rewarded with a “D” instead of an “F”, even if the student’s average is lower than that of some others who received “F” grades.

CLASSROOM DECORUM: You should not talk to other students when class is in session. Frequently I will address Math-related questions to the class at large, and I encourage you to respond to these questions freely, without raising your hand for permission. However, if you have any other sort of comment or question, I expect you to raise your hand and wait until you are called upon before speaking.

CELL PHONES: I expect you to TURN OFF YOUR CELL PHONE before class begins. Please note that “off” means OFF—not “vibrate” mode. If you are expecting a call that is so important to you that you feel you must answer it during class, then you should not come to class at all. If your phone rings during class and you have the audacity to answer it, then I expect you to immediately leave the classroom with your belongings and not to return until the next class meeting.

CALCULATORS: You may use any calculator you wish on both homework and exams. However, please be advised that you are expected to show all work involved in calculus operations (i.e. differentiation and integration). My best advice to you is to avoid calculators altogether except for basic arithmetic operations. Excessive reliance on your calculator will do you more harm than good.

INCOMPLETES: Please be advised that the so-called “I” grade (i.e., Incomplete grade) is almost never given. Do NOT expect to be able to avoid a low grade by requesting an Incomplete grade at the last minute. In order to qualify for an “I” grade, you must be (a) passing the course at the time the “I” grade is negotiated; (b) be so near the end of the course that you require no further instruction; and (c) have an excellent and documented reason for not being able to finish the course on schedule. Even in those very rare instances when an “I” grade is issued, it does not allow you to retake or replace any of the test scores you have already earned. It simply allows you to come back after the semester has ended to sit for the exam(s) missed at the very end of the term due to extenuating circumstances.

UNPAID STATUS: Even if you are expecting financial aid, it is your responsibility to ensure that you are properly registered, with fees paid by whatever deadline the College has established for you.

If you are not yet registered for this class, please be advised that the last day to register is Tuesday, January 10. If you have not registered by January 10, then you absolutely, positively, will not be able to register at all, because I do not sign override cards at any time for any reason.

If you see that you will be unable to pay your fees by your payment deadline, or if you fear that your financial aid may not be in place, then you should go to the Dean of Students’ Office to request an extension of your deadline. If your fees are not paid by the deadline, you will be voided from the roster and I will have to ask you to stop attending the class. I reiterate that, even if you are expecting some form of financial aid, payment of your fees is your responsibility. If you are voided from my roster for non-payment at any time after January 10, then you absolutely, positively, will not be able to reinstate yourself, because I do not sign override cards at any time for any reason.

COURSE OUTLINE

Please note: Test dates are given for your convenience only. I reserve the right to make changes in the test dates as needed. Any changes will be announced in class as early as possible.

WEEK CHAPTER/SECTION TOPIC

1 1.1 Definitions and terminology

1.2 Initial-value problems

2 2.2 Separable variables

2.3 Linear equations

3 (Monday, Jan. 16) HOLIDAY Martin Luther King Day

2.4 Exact equations

(Friday, Jan. 20) TEST Test #1 (§1.1, 1.2, 2.2, 2.3)

4 2.4 Exact equations

2.5 Solutions by substitutions

5 ---- Summary and review of classification techniques

3.1 Linear models

6 4.1.1 Initial-value and boundary-value problems

4.1.2 Homogeneous equations

(Friday, Feb. 10) TEST Test #2 (§2.4, 2.5, 3.1)

7 4.1.3 Nonhomogeneous equations

4.2 Reduction of order

8 4.3 Homogeneous linear equations with constant coefficients

4.5 Undetermined coefficients—annihilator approach

9 4.5 Undetermined coefficients—annihilator approach

4.6 Variation of parameters

(Friday, Mar. 3) TEST Test #3 (§4.1–4.3, 4.5)

10 4.6 Variation of parameters

4.8 Solving systems of linear equations by elimination

Reminder: Wednesday, March 15 is the last day to drop with a “W” grade.

11 5.1 Linear models: initial-value problems

12 6.1 Power series solutions about ordinary points

(Friday, Mar. 24) TEST Test #4 (§4.6, 4.8, 5.1)

13 6.1 Power series solutions about ordinary points

7.1 Definition of the Laplace Transform

7.2 Inverse transforms and transforms

14 7.2 Inverse transforms and transforms

7.3 Operational properties I

(Friday, Apr. 7) TEST Test #5 (§6.1, 7.1, 7.2)

15 7.3 Operational properties I

7.4 Operational properties II

(Friday, Apr. 14) HOLIDAY Good Friday

16 7.4 Operational properties II

(Friday, Apr. 21) TEST Test #6 (§7.3, 7.4)

17 (See Final Exam schedule) FINAL Final Exam (Comprehensive)