Department of Mathematics
Fall 2009
Math 282, Differential Equations, CRN 20767 (9:30-10:45 am, TR), and
Math 282HM, Differential Equations Honors Module, CRN 24541
Professor: Rick
Penn
Office: 24
Science West (SW)
(240)
567-5195
Rick.Penn@montgomerycollege.edu
http://www.montgomerycollege.edu/~rpenn
Office Hours: Mondays and Wednesdays, 11:00 - 11:50 am.
Tuesdays and Thursdays
9:00- 9:30 am
Other
times by appointment.
Course Description: An introduction to solving and qualitatively analyzing first order
differential equations; higher order linear differential equations and systems
of linear equations; solution by power series and numerical methods; the
Laplace transform and some applications.
PREREQUISITE:
A grade of C or better in MA 182 or equivalent, or consent of department.
If you enrolled and do not have the
prerequisites met, you may be dropped from the class.
Course Outcomes: Learning outcomes for this course were approved in Spring 2008. They can
be found on my website, or on the math department’s website.
Textbook: Differential Equations 3rd edition,
by Blanchard, Devaney and Hall, Thomson-Brooks/Cole
Publishing.
Calculator: You are required
to bring a graphing calculator to class every day. A TI-89 (or 92, which is functionally
equivalent) is highly recommended – these have some features that you will not
find on the lower numbered TI’s that will prove very useful to our
investigation of the differential equations.
Grades:
Tests: 3 x 20% = 60%
Quizzes: 20%
Final exam 20%*
* If
it will help your average, I will replace your lowest test grade with the score
you earn on the final.
If
your final average is 90% or higher, you will earn an ‘A’; 80-89% will earn a
‘B’; 70-79% will earn a ‘C’; 60-69% will earn a ‘D’ and 59% or lower will earn
an ‘F’.
Homework
will be assigned regularly, but will in general not be collected. This is not meant to imply that homework is
optional - quite the contrary, it is essential that you do all of the assigned problems!
If you pay careful attention in class, watch and understand as I explain
theorems and show examples, but then do not practice extensively at home, you will
likely find it very difficult to pass this class. You learn math by doing, not watching!
Make up policy:
Missed quizzes or tests will in
general not be made up after the
fact. However, I will try to make
alternate testing arrangements if
1) You notify me ahead of time that you must
miss the quiz/test, and it is for a college excused reason, and
2) We are able to arrange for you to make-up the
missed quiz/test before the next meeting of the class.
Under all other
circumstances, the missed grade will be recorded as a 0.
To
receive credit for the solution to any problem all work must be shown. A complete answer should be self-contained,
and include graphs, explanations in complete English sentences, and/or
tables, to help the reader (me!) to understand your answer.
Important dates: September 22: last day to drop the class (no ‘W’)
November 17: last day to drop the class (receiving a grade
of ‘W’)
December 17: final exam:
8-10 am (note the time! )
E-mail communications: Communications for this class, when
necessary, will be made via college e-mail.
Be sure to check yours often!
Math Science Center: Located in 02 Macklin Tower,
this is where you can go to borrow a math book, work in a group study area,
work in a quiet study area, use a computer for a math or science class, borrow
a calculator, or, best of all, get free tutoring. The phone number there is 240-567-5200, and
the hours are: Mon. – Thurs. 8am – 8pm, Fri. 8am – 4pm, Sat. 10am – 3pm. http://www.montgomerycollege.edu/Departments/mathscrv/
Accommodations for Students with Disabilities
Statement: Disability Support Services (240-567-5058)
Any
student who may need an accommodation due to a disability, please make an
appointment to see me during my office hour. A letter from Disability Support
Services (CB122) authorizing your accommodations will be needed. Any student
who may need assistance in the event of an emergency evacuation must identify
to the Disability Support Services Office; guidelines for emergency evacuations
for individuals with disabilities are found at: www.montgomerycollege.edu/dss/evacprocedures.htm
Academic Regulations & Student Code of Conduct
All MC students are expected
to follow “Academic Regulations” & “Student Code of Conduct” as described
in the MC Student Handbook. These
regulations and guidelines can be found at: www.montgomerycollege.edu/departments/academicevp/Student_PandP.htm
Inclement Weather
If
inclement weather forces the College or any campus or College facility to
suspend classes or close, public service announcements will be provided to
local radio and television stations as early as possible. You may also call MC
at 240-567-5000 or check the college website www.montgomerycollege.edu to verify MC school
closings. Any exams planned on days
classes are suspended will be administered at the first class meeting once
classes resume. Note that the Montgomery
County Public Schools (MCPS) and Montgomery College do not follow the same
school closing procedures.
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* * * * * * * * * * * * * * * * *
I would love nothing better
than to have everyone earn a passing grade, or better yet an 'A'. However, the grades that I give will be those
that are earned, as described above. If you "absolutely, positively, must
pass this class" to graduate / for
your job / to keep your full-time status/ so your dog doesn’t run away / or for
any other reason, the time to think about that is now, not after you have dug yourself into too deep a hole.
* * * * * * * * * * * * * * * * * * * * * * *
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I
expect that when you come to class, you are doing so with the intention of
learning. I will do my part to make the
atmosphere as conducive to learning as possible, and I ask you to do the
same. Feel free to ask questions, or to
answer questions for other students. But
please keep unnecessary distractions down, and,
please turn off and put away all cell phones, ipods, etc.
before entering class.
Math 282HM – Differential Equations with Honors Module
- Syllabus Addendum
Eligibility
for the Honors module requires completion of 12 academic credits at MC with a
GPA of 3.2 or better and a grade of ‘B’ or better in EN101/EN101A, or consent
of the campus Honors Program coordinator.
Overview: Students enrolled in MA282HM are expected to
complete all assignments and assessments given to students in the standard
MA282 course, and to master all learning outcomes associated with MA282. In addition, HM students will be expected to
meet regularly with the instructor outside of class time, complete additional
honors level work (described below), and master additional honors learning outcomes.
The requirement for all
Honors courses at MC is that enrolled students will produce a minimum of 30
pages of written material, or its equivalent; for this course, approximately
half of this requirement will be met through shorter assignments and work from
the book, and half will be through the presentation of your original
research. During our outside-of-class meetings,
you will receive additional instruction and guidance as you prepare for, and
eventually conduct, your research.
Research: Honors students will meet weekly with the
instructor out of class; early in the term these meetings will be as a group,
but as the semester progresses they may be more individual. During these meetings we will explore
extensions of the core topics presented in 282; we may discuss, for example,
discrete analogs of the continuous dynamical systems studied in class, nonlinear
systems, and what makes a dynamical system chaotic. By the mid-point of the term, each Honors
student will select a topic on which to conduct individual research for the
remainder of the term. This research
will culminate in the preparation of a term paper, 10-15 pages in length, and
an oral presentation to the class.
Non-linear dynamical systems, which are generally beyond the scope of
this course to fully analyze, provide several interesting topics which may be
selected for research, including chaos theory, turbulence, and the 3-body
problem. Other topics, inspired from
MA282 applications, may be selected as well.
Grading: Your grade will be determined as
follows:
Ø All tests, quizzes and other graded assignments given
to the standard MA282 section: 80%
Ø Honors assignments (short proofs and homework): 5%
Ø Research project:
15%
Note: the honors
work is NOT extra credit! Failure to satisfactorily complete all Honors
work will result in your class grade being lowered!
Honors Outcomes: The successful honors student will be able
to:
Ø Apply content from the course to a wider range of
applications than is expected of the non-honors students
Ø Select a topic related to content from the course and
analyze it at an appropriate depth.
Ø Present mathematical research in both oral and written
forms.
Tentative week-by-week
outline for the semester:
Week of Sections
to be covered (tentatively!)
8/31 Introduction, 1.1-1.2
9/7 1.3 - 1.5
9/14 1.6 - 1.7
9/21 1.8 - 1.9
9/28 Test 1, 2.1
10/4 2.2 – 2.3
10/11 2.4, 3.1
10/18 3.2 – 3.3
10/25 3.4, Test 2
11/1 3.5 – 3.6
11/8 4.1 - 4.2
11/15 4.3, Test 3
11/22 6.1 - 6.2
11/29 6.2 – 6.3
12/6 6.3, Special Topics, Review for Final
Final exam: Thursday,
December 17, 8-10am.
Math 282 Learning Outcomes
|
# |
Outcome:
Upon completion of this course/program a student will be able to: |
|
1. |
use qualitative and numerical
methods to analyze the family of solutions to a first-order differential
equation, particularly an autonomous equation |
|
2. |
solve first-order separable and
linear differential equations and corresponding initial-value problems |
|
3.
|
determine the domain of a solution
and describe long-term behavior of a solution |
|
4.
|
know and be able to apply the
theorem for existence and uniqueness of solutions to
a first-order differential equation |
|
5. |
write and solve a first-order
initial-value problem that models a practical situation involving a rate of
change |
|
6. |
rewrite a second-order differential
equation as a system of first-order equations |
|
7. |
use qualitative and numerical
methods to describe and analyze the family of solutions to a first-order
system |
|
8. |
write a first-order system in matrix
form, find the eigenvalues and write the general solution to the system |
|
9.
|
assume exponential solutions and solve
a homogeneous or non-homogeneous linear second-order differential equation
with constant coefficients |
|
10. |
understand and interpret the
solutions to a second-order equation in terms of harmonic oscillator |
|
11. |
use Laplace transforms to solve
first- and second-order initial-value problems when the differential equation
may be forced by a continuous or discontinuous function |
|
12. |
use an advanced software tool (Maple,
MATLAB, Mathematica, ODE software, and the like)
appropriately and effectively to aid in understanding the behavior
of solutions to differential equations |