Syllabus	Math 237: Differential Equations	Fall 2010

About this Course

Differential Equations: The name of this course, Differential Equations, suggests that we might somehow study equations involving derivatives. That is indeed what we will do. But more than just learning how to solve differential equations, we will learn how ``real-world'' phenomena can be fairly accurately described and studied with these new tools. We will explore the work of many who asked questions about the world around them and attempted to answer those questions using these tools. Questions like: What is the velocity required for a rocket to break free of the earth's gravity? Is there a way to accurately predict what the human population of a country will be in 10 years? How rapidly will a certain disease spread throughout an isolated region? How did a gentle wind cause the collapse of a massive concrete and steel suspension bridge? How long would it take to drain the Great Lakes (and how might that information be helpful)? What if I drilled a hole through the earth, through its center, and dropped a bowling ball in? Can the fluttering of the wings of a butterfly in Japan have a decisive effect on the weather in the United States six months later?We will look at some of these as well as other questions. In the end, perhaps we will even learn to ask questions that no one else has thought to ask.

Purpose: The primary purpose of this course is to help you develop a thorough understanding of the theory and methods of solving differential equations. But equally important, I hope that you will deepen your appreciation of the power and beauty of mathematics. I hope that you will take a cue from the mathematicians who have preceded you and discover yet new ways to apply your knowledge and creativity to solving the problems of the world we live in, and of the worlds we could live in.

Text: Fundamentals of Differential Equations, Seventh Edition by Nagle, Saff, and Snider. This text is very readable and it is expected that you will read it. We will start at the beginning, delving into most sections in Chapters 1, 2, 3, and 4. We will then pick and choose our way through Chapters 5, 6, 7, and 8. I hope we will always be able to dwell a bit on interesting problems.

Technology Use: A computer algebra system (CAS) or other graphing utility (such as certain graphing calculators) can be a useful tool in the study of differential equations. A CAS (Maple) will be available in most computer labs for your use. There are also tools available at the publisher's web-site. I will use some of these tools during class to demonstrate ideas. The use of certain of these tools may be allowed or required during some examinations. You should become familiar with them.

Assessment Policies

Homework: Homework will be assigned daily and collected weekly. Occasional "quizzes" may be given over assigned homework problems. After dropping the lowest score, the cumulative homework and quiz score will be weighted as worth 100 points (the same point value as an exam). Late homework will not be accepted.

Projects, Presentations, and Seminars: Completion and presentation of special projects will be required. Occasional in-class presentations of homework problems will also be required. Attendance at occasional Department-sponsored seminars may also be required. The cumulative point value for all projects, presentations, and seminars will be 100 points.

Exams: There will be 4 exams (some may have take-home components), each worth 100 points.

Final Exam: Note: Exam 4 will be given during the time scheduled for the final exam. Exam 4 will be a time-limited, 100-point exam, and will be non-comprehensive in nature.

Attendance And Make-up Policies: You are expected to attend every class, to arrive at class on time, and to stay for the entire period. A grade of zero will be assigned for any homework not submitted on time and for any quiz or exam not taken when administered to the class. The opportunity to "make-up" work missed will NOT be available except in instances required by The Colleges. In such cases, it is the student's responsibility to arrange for make-up work as soon as possible. (See HWS Catalogue, pp. 26-27.) In the event that I am required to provide "make-up" work, it may be significantly different from the work missed. This make-up policy will be strictly enforced.

Grading Scale: The exam scores, the projects/presentation/seminar score, the weighted homework/quiz score, and any bonus points earned will be added together. The total will be divided by 600 and the initial course grade calculation will be determined by the overall percentages:

The final course grade calculation will include consideration of factors such as attendance, conscientiousness, and level of participation. If your overall average falls in the upper 2% of a grade range, and you have 1 or fewer unexcused absences, and have been conscientious about projects, written work, and collected assignments, and have actively participated in class, you will have a "+" appended to your grade. On the other hand, if your overall average falls in the lower 2% of a grade range, you may have a "-" appended to your grade if you have at least 3 unexcused absences, or work has been missed or is incomplete, or if you have failed to participate at an acceptable level in class. Excessive absence (more than 3) may result in the loss of a letter grade.

Other

• Hobart and William Smith Colleges' Principle of Academic Integrity will be upheld. (See HWS Catalogue, p. 23. See also HWS Handbook of Community Standards.) Unless work is assigned collaboratively, you should not submit work for a grade that is not completely your own. Doing so will be grounds for receiving a failing grade in the course, and having a record of the event placed in your permanent file.

• All work submitted must be done in pencil, and must be detailed and neat (with all work shown) in order to receive full credit.

• A Note about the Center for Teaching and Learning (CTL): Hobart and William Smith Colleges encourages students to seek the academic collaboration and resources that will enable them to do their best work. The CTL offers a variety of resources that can help students achieve academic success. For more information on these resources, visit the CTL webpage at http://www.hws.edu/academics/ctl/index.aspx, or visit the CTL Blackboard site.

Disability Accommodations: If you are a student with a disability for which you may need accommodations, you should self-identify and register for services with the Coordinator of Disability Services at the Center for Teaching and Learning (CTL), and provide documentation of your disability. Disability related accommodations and services generally will not be provided until the registration and documentation process is complete. The guidelines for documenting disabilities can be found at the following website: http://www.hws.edu/disabilities . Please direct questions about this process or Disability Services at HWS to David Silver, Coordinator of Disability Services, at silver@hws.edu or x3351.