Math 225  Introduction to Differential Equations
Fall 2015  Syllabus  Matthias K. Gobbert
This page can be reached via my homepage at
http://www.umbc.edu/~gobbert.
Basic Information
 Matthias K. Gobbert,
Math/Psyc 416, (410) 4552404, gobbert@umbc.edu,
office hour: TuTh 01:0002:00 or by appointment
 Classes: SOND 103, TuTh 04:0005:15;
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.
Associated webpage:
http://store.doverpublications.com/048644595x.html.
List of errors:
http://umbc.edu/~rostamia/farlowerrata.html
This list is graciously maintained as benefit to us all
by UMBC colleague Rouben Rostamian;
if you find additional errors, please inform him at rostamian@umbc.edu.
 Grading policy:
Homework and Quizzes
 Test 1
 Test 2
 Test 3
 Final Exam

20%
 20%
 20%
 20%
 20%


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.
In particular,
Homework 0 is always due in the second class of the semester,
and some adjustments are necessary after Thanksgiving.
The homework will be collected, scored for completeness,
and some problems maybe for correctness.
There will usually be an individual quiz each week
that consists of one problem from the 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 a few unannounced group 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 nontechnical in nature.
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 acceptable late.
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 inclass exams;
to help you focus on what is relevant,
they are closedbook, closednotes,
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 and their coverage.
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 email, or in Blackboard.
You are responsible for checking
your UMBC email address sufficiently frequently.

Blackboard
is a course management system that allows for posting
and communicating among registered participants of a course.
We will actively use only the "Course Documents" area
and the "Discussion Board"
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 the "Course Documents" area.
The "Discussion Board" is for all contents questions;
for efficiency in communications, I cannot reply to emails
on contentsquestions; please post them in the "Discussion Board".
I will also use Blackboard to send email to the class,
which goes to your UMBC account by default.
Therefore, you must either check your UMBC email regularly
or have the mail forwarded to an account that you check frequently.
Course Description
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 firstorder and secondorder
ordinary differential equations. We will also cover
the solution by Laplace transforms and introduce systems
of firstorder 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.
Learning Goals
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
nonunique 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 firstorder 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.
Other Information
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
webpage www.umbc.edu/integrity,
the
UMBC Undergraduate Student Academic Conduct Policy
(PDF)
for undergraduate students,
or the
University of Maryland Graduate School, Baltimore (UMGSB)
Policy and Procedures for Student Academic Misconduct
(PDF)
for graduate students.
Copyright © 19992015 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.4, September 2015.