Math 225 - Introduction to Differential Equations
Fall 2009 - Matthias K. Gobbert
This page can be reached via my homepage at
- Matthias K. Gobbert,
Math/Psyc 416, (410) 455-2404, firstname.lastname@example.org,
office hours: MW 04:00-05:00 or by appointment
- Classes: SOND 105, MW 02:30-03:45;
please see the detailed schedule
for more information.
- Required prerequisites: a grade of C or better in Math 152;
recommended prerequisites: Math 221 and 251;
or instructor approval
- A copy of the following book is on reserve in the library.
This book is highly recommended as reference, but is not required.
The intention is to cover the material of the course sufficiently well
by the lectures, possibly complemented by specific reading assignments,
for which you can use the reserve copies in the library.
Stanley J. Farlow, An Introduction to Differential Equations
and Their Applications, Dover, 2006.
- Grading policy:
| Homework and Quizzes
|| Test 1
|| Test 2
|| Final Exam
A sufficient number of quiz scores will be dropped
in order to avoid penalizing infrequent absences.
Additional details or changes will be announced as necessary.
Announcements may be made in class, by e-mail, or in Blackboard.
You are responsible for checking
your UMBC e-mail address sufficiently frequently.
The homework assignments will be handed out in class.
The detailed schedule indicates
the planned number and section coverage of the homework assignments.
Working the homework is vital to understanding the course material,
and you are expected to work all problems.
Most of the homework assignments will not be collected, however,
they are preparations for the quizzes.
A few particular homeworks, such as the first one,
will in fact be collected and graded.
There will be two types of quizzes in this class:
On the due dates of homeworks, which is generally every Wednesday,
there will be individual quizzes
that test knowledge directly related to homework;
additionally, an individual quiz will be given on the first day
of the semester on some material that is critical to
your success in this class.
There will also be group quizzes, which
will generally be unannounced and brief.
They are designed to provide you
with quick feedback on your understanding of the material
and/or to generate class discussion;
there will be only few and they will count less than
the quizzes on the homework.
The tests and the final exam
are traditional in-class exams;
to help you focus on what is relevant,
they are closed-book, closed-notes,
and no calculators/computers allowed.
See the detailed schedule for the dates
of the exams and their coverage.
is a course management system that allows for posting
and communicating among registered participants of a course.
To log in, I suggest to go to myUMBC
and then use the Blackboard link on the left.
Then look for this course under "My Courses".
We will actively only use the "Course Documents" area.
I will post PDF files of the lectures for each class and
possibly appropriate additional notes in this area.
I will also use Blackboard to send e-mail to the class,
which goes to your UMBC account by default.
Therefore, you must either check your UMBC e-mail regularly
or have the mail forwarded to an account that you check frequently.
Introduction to Differential Equations is a first introduction
to the field of differential equations. Differential equations
are equations, that involve both a function and one or more
of its derivatives. The solution to a differential equation
is a function of one or more variables.
Differential equations arise in an extremely wide array of
application areas and are vitally important in the
sciences, engineering, and many other fields.
This course will stress scalar first-order and second-order
ordinary differential equations. We will also cover
the solution by Laplace transforms and introduce systems
of first-order ordinary differential equations.
This course will develop both a proficiency with the terminology
of differential equations and classical analytical solution techniques
for ordinary differential equations, with a brief exposure
to basic numerical techniques.
By the end of this course, you should:
understand and remember the key ideas, concepts, definitions,
and theorems of the subject.
Examples in this course include
the classification of differential equations,
solvability and uniqueness theorems,
and analytical solution techniques.
--> This information will be discussed in the lecture. You will apply and use them on quizzes, homework, and tests.
be able to apply mathematical theorems and computational algorithms
correctly to answer questions,
and interpret their results correctly, including potentially
non-unique solutions or breakdowns of algorithms.
Examples include choosing among several methods to solve
a differential equation and how to react to intermediate solutions found
that may indicate a break down of the method.
--> The class discussions, homework, and tests address these skills.
appreciate the power of mathematical abstraction and
understand how mathematical theory is developed.
The classical example of mathematical abstraction in this class is
the theorem that governs the number of fundamental solutions
for a linear ordinary differential equation of a given order.
--> These integration goals will be supported by the lectures.
be able to communicate orally by discussing mathematical ideas and algorithms
with the instructor as well as other students.
--> Group discussions and quizzes will contribute to this goal.
be able to communicate in writing effectively by using the notation
and terminology of the subject correctly.
--> Homework, group quizzes, and tests will give you feedback.
UMBC Academic Integrity Policy
By enrolling in this course, each student assumes the responsibilities of
an active participant in UMBC's scholarly community in which everyone's
academic work and behavior are held to the highest standards of honesty.
Cheating, fabrication, plagiarism, and helping others to commit these acts
are all forms of academic dishonesty, and they are wrong.
Academic misconduct could result in disciplinary action that may include,
but is not limited to, suspension or dismissal.
To read the full Student Academic Conduct Policy, consult the
UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity
or the Graduate School website
Copyright © 1999-2009 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.4, August 2009.