Engineering Mathematics IV:

Differential Equations

22m:34, Fall 2003

Syllabus

Instructor: Frederick M.Goodman
Office: 325G McLean Hall
Phone: 335-0791 (office)
email: goodman at math dot uiowa dot edu
Office Hours: To be arranged.

 

Course goals:

Knowledge of basic ideas and techniques of differential equations and applications.

 

Course web page:

www.math.uiowa.edu/~goodman/22m34/22m34.html

Assignments, course information, and electronic "handouts" will be provided on the web page.

 

Textbook:

Required text: Boyce and DiPrima, Elementary Differential Equations, 7th edition. ("Course Advantage Edition" with software CD.)

Note: the textbook includes a CD containing:

  1. An electronic copy of the entire text!
  2. An electronic copy of the student solutions manual. (So you should not purchase the solutions manual.)
  3. A program ODE Architect for exploring differential equations.
  4. An electronic copy of the lab book ODE Architect Companion.

Course plan:

We will cover much of chapters 1-4 and 6-7 of the text, with some additional material from other chapters if time allows.

Homework:

There will be weekly homework assignments which may require lots of time. You should allow an average of 6-8 hours per week for study outside of class.

Homework will be assigned on Tuesday of each week and will be due on Thursday of the following week. Note: I am allowing 2 full class sessions between the time that the homework is assigned and the due date. You are meant to get involved with the homework early, spend time on it, and figure it out. It is not appropriate for you to wait until the last moment and to depend on the instructor or others for solutions to the exercises.

Late homework will not be accepted.

Homework will include some work with computing, using the programs ODE Architect (which comes with the textbook) and Mathematica (which is available on university computers).

Computing work:

There are several reasons to use computers in studying (and, later, in applying) differential equations.

One reason is that certain computations are in principle straightforward, but tedious; you ought to know how to do them by hand, but then you might as well do them by machine. After the course, presumably you would generally choose to do such computations by machine.

A second reason is that other computations are impossible to do by hand. Frequently, differential equations cannot be solved explicitly by hand. However, one can still find numerical (and graphical) solutions, which can be just as useful in practice as an explicit symbolic solution.

A third reason is that computers can provide graphical representations of differential equations and their solutions which are of great help for understanding the behavior of the equations and solutions.

You should start early on the computing work in order to anticipate the inevitable glitches -- the mysterious syntax errors or the last minute unavailability of the printer.

Computing Resources:

I will arrange accounts for you on the math department computing network. You can use the lab in MLH B5; your university ID card will serve as a key for this room. This lab has machines running Linux. Of course, you can also use the engineering computing labs.

The university has a site license for Mathematica, and Mathematica is available on the math department network, on the engineering computers, and at other sites on campus. Mathematica runs on all common platforms: Windows, Mac, Linux, etc.

A student version of Mathematica is available for use on your own personal computer at a considerable discount ($140). The current version is 5.0.

In principle, you could also do the computing work using Maple, which is a similar large program combining symbolic, numeric and graphical capabilities. However, I am not very familiar with Maple, and will not be able to help you with it.

The program ODE Architect supplied with your textbook runs only on Windows machines. You can install and run it on your own machine, or you can run it on university machines from the CD (without installing).

 

Exams and grading:

There will be two midterm exams on dates to be arranged. There will be a comprehensive final exam on the date specified in schedule of courses.

Grades will be weighted as follows: Midterm exams, 100 points each. Final exam, 200 points. Homeowork: 100 points. (In practice, I will average your scores using several similar weighting schemes and give you the best possible deal.)

Attendance and absences:

Regular attendance will be expected. However, if you must miss class, you will still be responsible for the material discussed in class. You are responsible for announcements made in class, which may concern changes in the assignments, syllabus, exams, etc.

Absence from exams will require a compelling reason, and must be arranged in advance.

Accomodations for students with special needs.

Students with disabilities are entitled to special arrangements; please contact me in order to arrange appropriate accomodations. (Requests for modifications of class requirements or testing must be made through the Student Disability Services office, 3100 Burge Hall.)

Complaint procedure:

I hope and expect that you will have a good time, work a lot and learn a lot in this course. If you have concerns or complaints about any aspect of the course, please discuss these with me. If we are not able to resolve the difficulty, please contact the Chair of the Department of Mathematics, room 14 Maclean Hall.

Fred Goodman
Fall, 2003