Math 225 - Introduction to Differential Equations
Spring 2020 - Syllabus - 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: TuTh 01:00-02:00 or by appointment
- Classes: SHER 151, TuTh 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 library reserves.
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 rule:
| Homeworks and Quizzes
|| Test 1
|| Test 2
|| Test 3
|| Final Exam
Additional details or changes will be announced as necessary.
See also general rules and procedures
for more information.
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 due date of each homework and its intended coverage.
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 Thursday,
but watch the actual due date stated in the detailed schedule,
as adjustements are typically necessary at some point.
The homework will be collected, scored for completeness,
and some problems maybe for correctness.
You have a choice for each homework submission:
Either submit a paper copy at the beginning of class on the due date,
or submit an electronic copy online as one PDF file
in the Assignments area of our Blackboard site.
For online submission, you must submit one PDF file
for each Problem 1, 2, etc. separately, not a combined file!
There will also be a few unannounced in-class quizzes
using learning groups formed by the instructor.
For instance, they may be designed to initiate class discussion
or to give me feedback on your learning.
They may be technical or non-technical in nature.
An individual Quiz 0 will be given on the first day
of the semester on some material that is critical to
your success in this class.
Late submission of homeworks, except Homework 0,
cannot be accepted under any circumstances
due to the organizational difficulties associated
with the communcation with the grader.
Homework 0 is required of all students and is accepted late.
Homework 0 must be submitted online as one PDF file
in the Assignments area of our Blackboard site.
A sufficient number of homework and quiz scores will be dropped
in order to avoid penalizing infrequent absences.
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; only the ones provided by me are allowable;
they will be the ones from the front and back inside covers
of the textbook by Farlow.
See the detailed schedule for the dates
of the exams.
We will use the course management system
for posting of all material
(including homework, class summaries, PDF transcripts, handouts),
for links (to tapings of lectures),
for online submission of homeworks and quizzes.
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.
Do not use Blackboard to message me,
since I may not find it in a timely fashion;
rather use conventional e-mail to my UMBC address listed above.
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 homeworks, quizzes, 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.
have experience working actively with peers in a group,
both on the scale of the class and in a smaller team.
Group work requiring communication for effective collaboration
with peers and supervisors is a vital professional skill,
and the development of professional skills including this networking
is a declared learning goal of this course.
Additionally, getting to know other students as part of learning groups
will prove invaluable for homework and tests.
--> Group discussions and quizzes will contribute to this goal.
UMBC Statement of Values for Academic Integrity
Academic integrity is an important value at UMBC.
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 webpage on Academic Integtrity at
UMBC Undergraduate Student Academic Conduct Policy
for undergraduate students,
UMBC Graduate School Policy and Procedures for Student Academic Misconduct
for graduate students.
Copyright © 1999-2020 by Matthias K. Gobbert. All Rights Reserved.
This page version 2.0, April 2020.