MATH 210: Differential Equations with Applications



Mathematics Department, Bryn Mawr College, Fall 2012




Professor: Victor Donnay

Lecture: Tues/Thur  11: 15-12: 45 


 Park Rm. 338


Office: Park #330


Phone:   610-526-5352


Office Hours: tba




Co-requisites: You should have taken or presently be taking either Multi-variable Calculus or Linear Algebra. Please speak to me if this is not the case for you. 


Text: Differential Equations by Blanchard, Devaney, and Hall, 4thedition, 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 re-assessment. If on the re-assessment, 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 non-linear systems and how feedback effects in non-linear 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 self-sufficient 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 how mathematics is involved.


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.




There will be a mid-term exam, a final exam and a final project. The tentative schedule for the exams is:


Take-home Midterm exam: in the 6th week: Oct 8-12.


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). Students are encouraged to submit a draft of their project by Tuesday December 4th. For any project submitted by this date, I will give you feedback on how to improve the project that you can use to revise and resubmit by the Dec 13th deadline.




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. 




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 Resubmission:  If you get less than perfect on the quiz, you are welcome to redo the problem(s) you got wrong and resubmit your work to be re-assessed. If correct it will be given full credit. You must staple your new work to your original quiz sheet and submit both together (so I can see that you have fixed your earlier mistake). You must also write out a brief description of what your mistake was and what you need to remember so you will not repeat this mistake again. Research into how people learn indicates that this type of reflection on one's learning leads to improved learning.


If this explanation is not included, your quiz will be returned without being re-assessed.




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 role-playing simulation game that applies aspects of differential equations to a real world situation. This will require a three-hour 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




Final Project


Final Exam







Topics Covered in my spring 2011 Offering of Differential Equations: