ORDINARY DIFFERENTIAL EQUATIONS
Department of Mathematical Sciences
WORCESTER POLYTECHNIC INSTITUTE
MA 2051, Ordinary Differential Equations, Term C03
Main Instructor:
B. Doytchinov
Office: SH105D
Office hours:
MoFr 1:00-2:00pm; TuTh 10:00-11:00am and by appointment.
e-mail:bogdand@wpi.edu
Teaching Assistant:
Daniel Pulido
Office: Stratton Hall 204
Phone: 831-5546
Office Hours:
Tu 12:00-2:00pm; Th 1:00-2:00pm
e-mail:pulidod@wpi.edu
TEXT
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Paul Davis, Differential Equations, Modeling with Matlab, Prentice Hall.
COURSE CONTENTS
This is a first course in differential equations.
The main skills that you will learn, and on which you will be evaluated
are:
- formulate differential equation models from conservation laws;
- set up second order differential equation models for oscillating
systems;
- sketch solution curves using only the differential equation
(no solution formula, no computer);
- identify stady-state solutions and determine the stability of these
solutions;
- use basic universal numerical and analytic methods to approximate
solutions of differential equations;
- solve separable differential equations via integration;
- solve first order linear equations using different methods;
- solve second order, constant-coefficient differential equations using
characteristic functions, undetermined coefficients, and variation of
parameter.
- compute phisical quantities such as amplitude, period, natural frequency,
resonant frequency, and amplitude at resonance for forced spring-mass systems;
- solve first order linear systems of differential equations with constant
coefficients;
- sketch phase portraits and classify singularities of first order linear
systems.
LECTURES and CONFERENCES
You are supposed to spend 15 hours per
week on this course. Of these, you will be spending 5 hours per week
in class: three hours of lectures, and two conference sessions.
The other 10 hours must be devoted to studying on your own: reading the book,
reading and organizing your notes, solving problems. You are supposed to
attend all lectures and conferences. If you miss a class, it is your
responsibility to make a copy of the classnotes from another student and
make sure you learn what you have missed.
Lecture notes will be posted
on the web
in advance. Please print them out and
bring them to class. These notes are intentionally incomplete; we will be
filling in the blanks in class.
HOMEWORK and QUIZZES
Homework is assigned for each section of
the book covered and posted
on the web.
Homework is a required component of the course.
Working the exercises will help you learn, and give you some perspective on
your progress. You are encouraged to discuss homework problems with each other.
Homework will never be collected or graded, but, during every
conference there will be a short mini-quiz on one of the homework
problems. There will be 12
quizzes altogether and the ten best scores will count toward the final
grade (see below); the two lowest quiz grades will be dropped.
The problems of the tests will be similar to the ones
assigned as homework.
EXAMS and GRADING POLICY
There will be four in-class tests.
Each test will take 40 minutes. All tests and qizzes are closed-book.
No notes, books, calculators or computing devices of any sort are allowed.
If you miss a test for a documented legitimate reason (illness,
family emergency, participation in university-sponsored event, etc.),
you will be given the opportunity to take a make-up test on
February 26, in class. No other make-ups will be given.
Your final grade will be calculated in the following way:
90% of the grade come from the four Tests,
10% of the grade come from the 10 best mini-quiz scores.
You will be given the opportunity to earn extra bonus points
that will be added directly to your final score. These will
come from in-lecture activities and surveys. Keep alert for
announcements.
These scores are combined to give a final number of
points, between 0 and 100.
Point ranges for the final grades are approximately given by:
A: 100-90
B: 89-80
C: 79-65
These cutoffs might go down a bit due to curving, but not by much. They
will not go up. (In other words, 90 points guarantee you an A, etc).
Ordinary Differential Equations, Term C03
Schedule, Lecture Notes, and Homework
The Teaching Team
This syllabus and the schedule as
PostScript
or
pdf
Notes and Other Materials
Send me mail:
bogdand@wpi.edu