Math 225 - Introduction to Differential Equations
Spring 2011 - 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 hour: W 01:30-02:30 or by appointment
- Classes: AC IV 145, MW 04:00-05:15;
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.
List of errors:
This list is graciously maintained as benefit to us all
by UMBC colleague Rouben Rostamian;
if you find additional errors, please inform him at email@example.com.
- Grading policy:
| Homework and Quizzes
|| Test 1
|| Test 2
|| Test 3
|| Final Exam
Late assignments cannot be accepted under any circumstances
due to the organizational difficulties associated
with the communcation with the grader.
A sufficient number of homework and 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 posted in
the Blackboard site of our course; see below.
The detailed schedule indicates
the intended number and section coverage of the homework assignments,
but the postings in Blackboard are the final reference.
Working the homework is vital to understanding the course material,
and you are expected to work all problems.
Most homework assignments will be due on Wednesday,
but watch the actual due date stated on the assignments.
Homework 0 is always due in the second class of the semester.
The homework will be collected, scored for completeness
and some problems for correctness.
There will occasionally be quizzes.
Some may be individual quizzes,
whose material is directly related to homework;
others may be group quizzes designed to provide you
with quick feedback on your understanding of the material
and/or to generate class discussion;
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.
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.
One sheet of integral tables and one sheet of Laplace transforms
are allowable aids and will be provided in class.
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.
We will actively only use the "Course Documents" area
of our course in Blackboard.
I will post class summaries and PDF files of the lecture notes
as well as other material including the homework assignments 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.
Additionally, I will show how to use the software package
Matlab to help with some of tasks in this class.
Matlab is the -- by far -- most popular mathematical software tool,
used in fields ranging from mathematics, statistics, engineering,
physical, natural, and life sciences, to economics and business.
I use Matlab myself in my professional life, and the idea is to
demonstrate how professionals use software tools
effectively and appropriately.
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 breakdown 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.
Classical example of mathematical abstraction in this class are
the existence and uniqueness theorem for first-order initial value problems and
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 effectively by discussing mathematical ideas and
algorithms with the instructor as well as other students.
--> Group discussions and quizzes will contribute to this goal.
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
UMBC Undergraduate Student Academic Conduct Policy
University of Maryland Graduate School, Baltimore (UMGSB)
Policy and Procedures for Student Academic Misconduct
for graduate students.
Copyright © 1999-2011 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.3, January 2011.