Differential Equations I Fall 2006 (2nd half), Math 13 (http://www.math.hmc.edu/math13b) Section 1 MWF 10, Jacobs B134 Section 2 MWF 11, Jacobs B134 Prof. Darryl Yong, Olin 1265, dyong@hmc.edu Office hours: Wed 1-4 pm, and other times by appointment AE Tutoring hours: Sun, Tue, Thu 8-10 pm in Riggs Room at LAC

Course description

Math 13 introduces students to differential equations, their use as models for physical systems and methods for their solutions. This course will concentrate on first-order and second-order equations and their applications to mathematical physics (e.g., mass-spring systems) and population biology.

Topics covered: Classification of ODEs, Direction Fields, Modeling Physical problems with ODEs, Separable Equations, Integrating Factors, Change of Variables, Numerical Methods and ODE Architect, Existence and Uniqueness, Linear Second-Order Equations with Constant Coefficients, Method of Undetermined Coefficients, Variation of Parameters, Higher-order Equations and an Introduction to Systems of ODEs

Our textbook, Differential Equations: A Modeling Perspective (2nd ed) by emeritus HMC professors Robert Borrelli and Courtney Coleman is available at Huntley Bookstore.

Grading

Homework

Homework assignments wil be announced on this webpage and will generally be due on Wednesdays and Fridays. Late homeworks will not be accepted except incases of family or medical emergencies. Your lowest homework score will be dropped when computing your homework average.

Being able to direct your own learning is an important skill that I hope you will develop while at Harvey Mudd College. One component of being a self-directed learner is the ability to monitor your own understanding. To help you develop this ability, each problem on your homework assignments will be marked as being optional or required. Any optional homework problems that you complete and turn in will be graded. Your homework score will be reported as the number of points earned on attemped problems divided by the total number of points for required and attempted optional problems. Last year, students who completed optional problems on average scored one letter grade higher than those that did not, so it is to your advantage to at least try these problems.

I recommend that you read all of the assigned problems before working on any of the problems to see if you can do them by yourself. If you're not yet ready to try the problems, read the book more carefully, talk to your classmates or instructor, or ask for help from an AE tutor. If you feel you need less practice on a particular concept or type of problem, you may decide to skip some of the optional problems. If you need more practice, you can try doing some unassigned problems whose answers are in the back of your textbook. (Don't turn these unassigned problems in.)

You are encouraged to work cooperatively on your homework assignments with your classmates. However, every student MUST write up his/her own homework separately. In addition, you must cite any sources of help that you use. If you work with one of your classmates on a problem, be sure to acknowledge that person in your homework write-up; if you use any published source besides our textbook, acknowledge that too. Harvey Mudd's honor code is in effect for all students in this course.

Communicating mathematics well is just as important as being able to do it. Every assignment should be written up neatly with explanatory prose where necessary. What is obvious to you may not be obvious to others, and graders may take points off for writing that they can't read or understand easily. You may find these guidelines and examples of good and bad mathematical writing helpful.

The following table contains materials for our course in Adobe Acrobat (.pdf) format.

Lecture notes and calendar

The following table is a tentative schedule for our class. Section numbers relevant to lecture are shown in parentheses; please read these sections before coming to class. Lecture notes will appear as links in this table after class.