**Lecture:** TuTh 11:00-12:15 CBA 105

**Instructor:** Mark Brittenham

**Office:** Oldfather Hall (OldH) 819

**Telephone:** (47)2-7222

**E-mail:** mbritten@math.unl.edu

**WWW:** http://www.math.unl.edu/ ~ mbritten/

**WWW pages for this class:** http://www.math.unl.edu/ ~ mbritten/classwk/221s03/

(There you will find copies of nearly every handout from class, lists of homework problems assigned, dates for exams, etc.)

**Office Hours:** (tentatively) Mo 11:00-12:00, Tu 2:00 - 3:00, We 10:00-11:00,
and Th 1:00-2:00, and whenever you can find me in my office and I'm not
horrendously busy. You are also quite welcome to make an appointment
for any other time; this is easiest to arrange just before or
after class.

**Text:** *Fundamentals of Differential Equations*, by Nagle,
Saff, and Snider, Fifth edition, Addison-Wesley (2000).

This course, as the name is meant to imply, is intended to introduce
you to some of the problems, techniques, and applications of differential
equations (i.e., problems involving an (unknown) function and some of its
derivatives). Developing and solving such equations is a fundamental part
of many science and engineering problems. We will explore several different
approaches to differential equations, which depend on different interpretations
of the word `solving'. The course will focus on analytical methods (finding a formula),
qualitative methods (understanding the basic shape of the *graph* of
a solution), and numerical methods (finding approximate solutions, largely
with the help of a computer).

Our basic goal will be to work through some or all of each of the following chapters:

Ch. 1, Introduction

Ch. 2, First Order Differential Equations

Ch. 3, Mathematical Models and Numerical Methods

Ch. 4, Linear Second Order Equations

Ch. 5, Systems and Phase Plane Analysis

Ch. 6, Higher-order Linear Differential Equations

Ch. 7, Laplace Transforms

**Homework** will be assigned from each section, as we finish it.
It is an essential ingredient to the course - as with almost all of
mathematics, we learn best by doing (again and again and ...). Cooperation
with other students on these assignments is acceptable, and even
encouraged. However, you should make sure you are understanding the
process of finding the solution, on your own - after
all, you get to bring only one brain to exams (and it can't be someone
else's). For the same reason, I also recommend that you try working
each problem on your own, first. Homework will not be collected, and therefore, not
graded (the solution to every odd-numbered problem may be found at the
end of the book); but it is probably the most important ingredient toward making
sure that you are understanding the material..

In addition, we will have one significantly larger assignment. This **project**
will be assigned near the end of February, and be due several weeks later.
You may choose to work on the project in groups of up to three, with one write-up
turned in for the group, or you may choose to work on it individually. It will
count 10% towards your final grade.

**Quizzes** will be given each Thursday, during weeks that do not
also contain
an exam (in *our* class...) or the first day of classes. Each will
typically consist of one
question (modelled on a homework problem) from the material covered through
the previous Tuesday. Your lowest two quiz grades will be dropped before computing your
final quiz average, which will constitute 20 % of your grade. A missed quiz will
count as zero (and will therefore be the first grade dropped); a make-up quiz can
be arranged only under the most unusual of circumstances.

**Midterm exams** will be given two times during the
semester, approximately every six weeks - the specific dates will
be announced in class well in advance (likely candidates: mid February,
end of March). Each exam will count 20% toward your grade.
You can take a
make-up exam only if there are compelling reasons (a doctor SAYS
you were sick, jury duty, etc.) for you to miss an exam. Make-up
exams tend to be harder than the originals (because make-up exams
are harder to write!).

Finally, there will be a regularly scheduled **final exam** on
Friday, May 9, from 10:00am to 12:00noon.
It will cover the entire course, with a slight emphasis
on material covered after the last midterm exam. It will count the
remaining 30% toward your grade.

**Your course grade** will be calculated numerically using the above percentages,
and will be converted to a letter grade based partly on the overall average of the
class. However, a score of 90% or better will guarantee some kind of **A**, 80%
or better at least some sort of **B**, 70% or better at least a flavor of
**C**, and 60% or
better at least a **D**.

And now the obligatory pep talk:

In mathematics, new concepts continually rely upon the mastery
of old ones; it is therefore essential that you thoroughly understand each
new topic before moving on. Our classes are an important opportunity for you to ask
questions; to make
__sure__ that you are understanding concepts correctly.
Speak up! It's
__your__ education at stake. Make every effort to resist
the temptation to put off work, and to fall behind. Every topic has to be gotten
through, not around. And it's alot easier to read 50 pages in a week than it is
in a day. Try to do some mathematics every single day. (I do.)
**Class attendance** and **doing the homework** are probably your best
methods for insuring that you will keep
up with the material, and to make sure that you understand all of the
concepts.

**Departmental Grading Appeals Policy:** The Department of
Mathematics and Statistics does not tolerate discrimination
or harassment on the basis of race, gender, religion, or sexual orientation.
If you believe you have been subject to such discrimination or harassment,
in this or any other math course, please contact the department.
If, for this or any other reason, you believe your grade was assigned
incorrectly or capriciously, then appeals may be made (in order) to
the instructor, the department chair, the department grading appeals
committee, the college grading appeals committee, and the university
grading appeals committee.

**Jan. 13** First day of classes.

**Jan. 20** Martin Luther King Day - no classes.

**Jan. 24** Last day to withdraw from a course without receiving a **`W'**.

**Mar. 7** Last day to change to or from P/NP.

**Mar. 16-23** Spring break - no classes.

**Apr. 11** Last day to withdraw from a course.

**May 2** Last day of classes.

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