MATH 210:
Differential Equations with Applications
Syllabus
Mathematics Department, Bryn Mawr
College, Fall 2012
Professor: Victor Donnay 
Lecture:
Tues/Thur 11: 1512: 45
Park Rm. 338

Office: Park #330 

Phone: 6105265352 Email: vdonnay@brynmawr.edu 
Office
Hours: tba 
Corequisites: You should
have taken or presently be taking either Multivariable Calculus or Linear
Algebra. Please speak to me if this is not the case for you.
Text: Differential
Equations by Blanchard, Devaney, and Hall, 4^{th}edition, published by
Brooks/Cole.
Course Web
Site: accessible
from Prof. Donnay's
homepage
All
materials for the course will be found on the web site or at the course
Moodle site.
My Teaching Philosophy:
The world is facing many difficult problems and needs thoughtful people with strong math skills (among other talents) to work on solving these problems. My goal is to support you to develop the skills you need to be prepared to help address the problems facing our world.
People learn at different speeds and in different ways. My aim is for you to learn the as much of the material in our course as possible by the end of the semester. If there is a topic you did not fully understand at one point in the course, I would like to encourage you to keep working and trying to understand it.
Ability in math is not a fixed skilled. You can improve your ability through practice (just like an athlete in sports improves with practice). The brain is very malleable and can continue to form new neural connections throughout one's lifetime. It is the formation of these neural connections in the brain that constitute learning. In short, by working at it, you get smarter.
As much as you are willing to work hard and keep making the effort to improve, I am going to support you. I do this by using an assessment approach that gives you more than one chance to demonstrate mastery of a topic. On the weekly quizzes and midterm, I offer a redo option. If there is a topic you have not yet mastered, you can continue working to learn it and then take a reassessment. If on the reassessment, you demonstrate mastery of the topic, I will give you credit for this improved performance in determining your grade.
Goals of the
Course: In this
course, you will:
Do mathematical modeling
which involves studying real world situations using mathematics; in our case,
particularly using ordinary differential equations.
Learn to recognize real world
problems that are or could be examined using mathematical modeling. Be aware of
the power but also the potential weaknesses in using mathematical
modeling.
Develop an understanding of
linear and nonlinear systems and how feedback effects in nonlinear systems
can lead to unexpected behaviors.
Examine differential
equations using graphical (qualitative), numerical and analytical methods.
Communicate your mathematical
reasoning in writing and verbally.
Develop your ability to work as
an independent and selfsufficient learner:
What
to do when you do not know what to do
How
to take what you have learned in one situation and apply it to a new and
different situation (transfer of knowledge)
Get
comfortable with not knowing the answer immediately
Learn
material we have not covered in class by reading the book and applying this
newly learned information to solve problems.
Become
part of a community of learners who support, encourage and learn from one
another.
We
will cover most of the following sections from Blanchard et al:
Ch.1:
Section 1, 2, 3, 4, 5, 6, 7, 8, 9
Ch.
2: Section 1, 2, 3, 4, 5
Ch.
3: Section 1, 2, 3, 4, 5, 6, 8
Ch.
4: Section 1, 2
Ch.
5: Section 1, 2
Ch.
7: Section 1, 2, 3, 4
Appendix
B.
Plus
additional topics as time and interest permits.
The topics from the last time I taught the
differential equations course are listed at the end of the syllabus to give you
a sense of what we will cover.
Additional Reading: In addition to our text, we will have occasional supplementary readings that show how the material we are learning in the course relates to real world issues and there will be homework assignments involving the reading.
Students will be expected to find two articles, over the course of the semester, that relate to mathematics and post them to the class wiki with a short write up describing
Computer
Assignments:
There will be extensive use of the computer during the course both during class time (with laptops) and as part of homework assignments. We will use the software DE Tools that comes with the textbook. You will be encouraged to "play around" with the modules in this program to develop a graphical understanding of the concepts in our course.
We will
also use and write simple programs (possible systems include Excel,
Mathematica). No previous computer experience is necessary or assumed.
Exams:
There
will be a midterm exam, a final exam and a final project. The tentative schedule
for the exams is:
Takehome Midterm exam: in the 6^{th } week: Oct 812.
Final Project: Due at the start of the last class of the semester, Thur Dec 13th.
Students
will work in teams on a project of their choosing. The project might involve
using material from the course to study an applied situation, examining a
theoretical issue in more depth or studying a topic that extends the material
from the course. Projects will be written up in the form of a paper (10  15
pages).
Homework:
Homework
will be assigned for each class and will be collected once a week on Tuesday.
Each student may have two late homeworks with no questions asked. You must submit the late homeworks by the next class. Once you have used up your two late homeworks, other late work will not be accepted unless
there is a special situation (ex. serious medical problem) and you get my
permission ahead
of time.
The homework problems are assessed on the following scale:
When you get your homework back, you should look through the problems and see what you have not yet mastered. Those topics are where you should spend your effort studying.
HW Redo option: Each week, you may choose one problem that you did not Master and redo the problem and resubmit it the following Tuesday. You should attach the resubmission to the inital hw so you grader can see the progress you have made. With the redo problem, you must also state what you did differently in the redo than in the initial submission and what you learned that you had not understood the first time. If the redo shows improvement over the original submission, the grader will revise your score on that problem.
The
best way to learn mathematics is by doing lots of problems. Do not limit
yourself to just doing the problems that you are required to hand in. You
should do some problems after each class. This way, the next lecture will make
a lot more sense. Do not wait till the last minute and do all the problems at
once. You will have much more trouble understanding the lectures and will
therefore be using your time inefficiently.
You are encouraged to collaborate on
homework. This means you can talk with each other, figure things out together,
help each other. But when you finally write up your answer, you should do this
by yourself. You may not copy the answer that someone else has written. This
would be a violation of the honor code.
Quizzes:
There
will be a short quiz each week to give you feedback on your progress. It will be a take home quiz handed out on Tuesday and due at the start of class on Thursday. The quiz will deal with material from that week's homework.
Quiz
If this explanation is not included, your quiz will be returned without being reassessed.
Classroom:
During
class, there will be a mixture of lecturing by the professor and time spent by
the students working out problems and discussing their results in groups.
Research has shown that this type of active participation leads to improved
learning.
The
group work does not go well when members of the group are absent. Therefore it
is important that you attend to class. Please be respectful of your fellow
students.
If
you decide to take this course, you must commit to attending class regularly. Attendance will be taken and substandard attendance will be taken into account
in determining grades.
Special
Event:
The class will carry out a roleplaying
simulation game that applies aspects of differential equations to a real world
situation. This will require a threehour time block and will take place during
an afternoon or evening in the third or fourth week of the semester. More
details will be forthcoming.
Final grades will be
determined using the following percentages:
Homework, quizzes, class
participation 
25% 
Midterm 
25% 
Final Project 
25% 
Final Exam 
25% 
Total 
100% 
Topics Covered in my spring 2011
Offering of Differential Equations: