s214S09.htm

Syllabus: Math 214 - Elementary Differential Equations

Spring 2009

Instructor: Dr. Stephen Saperstone, ST1-247; TEL: 703.993.1486; Math Dept: 703.993.1460; FAX: 703.993.1491; My Home (to be used in emergencies):
Course Website: http://math.gmu.edu/~sap/S09/m214/214S09.html
E-mail: sap@gmu.edu

Office hours: MW 14:00 -15:00 and by appointment in ST1 - 247
Course Objectives:

Development of specialized techniques for solving first and second order ordinary differential equations (ODEs) by analytical methods such as separation of variables, integrating factor methods, power series, Laplace transforms, and matrix algebra.
Squeeze as much information as possible out of an ODE without ever solving it. This is important even when a "closed form" solution is possible. Examination of the analytical and graphical properties of direction fields are used here. Computer graphic software also serves to aid in this analysis.
Development of basic numerical approximation methods for solving initial value problems. This too is important even when a "closed form" solution is possible. Control of error is emphasized.
Illustrate by example of how to model "real world" phenomena with ODEs. Examples are drawn from population dynamics, electric circuits, sports, mechanics, chemical processes, and economics.
See the "big picture" and interpret (in words) the meaning of mathematical formulae, expressions and graphs.

Course Materials: There is no textbook. All material is available online at the course website.
Homework: Check the course web site for homework assignments. Approximately 4 homework exercises are assigned for each lecture and are generally due two lectures later. Each one is graded on a scale from 0 to 4 points. Five (5) points will be awarded in the case of an exceptional solution. I will drop the lowest two homework assignment scores when making up final grades. These are exercises to work in order for you to keep up with the lectures and to prepare for tests. If you expect to be successful in the course, you should be regularly working these problems and many more throughout the semester. I will post solutions to many of the problems at the course web site.

Software: I will use Maple to and some online java applets to calculate symbolic solutions to some ODEs as well as to demonstrate qualitative behaviors of solutions. Some homework exercises will require Maple solutions.

Exams: Three (3) midterm exams and a comprehensive final exam: tentative dates:

Exam 1	23 February
Exam 2	01 April
Exam 3	29 April
Final Exam	06 May @ 13:30, IN 103

Exam questions will stress both problem solving AND conceptional understanding. All exams have approximately 25 "bonus points."You can accumulate these points for the average grade on the three midterm exams.

Problem Sessions: I will hold a problem session on most Fridays at 12:30-13:20 for the express purpose of reviewing solutions to the homework exercises. Notice for problem sessions will be posted in a timely fashion at the course website. Attendance is optional but is highly recommended.

Determination of Final Grade: Grades are based on the following distribution of credit

Homework	15%
Exams (3 @ 20%)	60%
Final Exam	25%

Grading Scale: See the following table.

A+	A	A-	B+	B	B-	C+	C	C-	D	F
∞ - 99	98 - 92	91 - 90	89 - 88	87 - 82	81 - 80	79 - 78	77 - 72	71 - 69	68 - 60	59 - 0

Make-Ups: There will be none! If you miss an exam due to a legitimate reason - which you will have to justify to me (e.g., illness), then the final exam will be used in its place.

Academic Integrity: All exams are to be done without any assistance from anyone else. Your work here is governed by the GMU Honor Code at all times.
Updates: Check the web site for updated information regarding exam dates, homework assignments, and exercise hints/solutions.

How to Succeed in this Course:

Read the assigned section before each lecture and attend all lectures. Twelve-Fifteen (12-15) hours per week may not even be enough study time for many of you.
Have a pencil & writing tablet with you as you read the lecture notes. Cover up the solution to the worked out examples before you read the solution. If you get stuck, just read how to proceed. Don't read the whole solution until you are truly jammed.
Try all of the assigned exercise first without looking at the solutions. Then try many more exercises than the assigned ones. All the solutions are posted at the website As a colleague of mine once said "Mathematics is not a spectator course."
Success in ODEs requires that you have mastered and synthesized most of the topics of the calculus. Topics that you might have understood, like continuity & differentiability, power series, implicit functions, differentials, partial fractions, can come back to haunt you.

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