Math 232A
Engineering Mathematics
Fall, 2007

Syllabus


Course topics.   MATH 232 completes the required sequence of mathematics courses in the first two years of the engineering program at Calvin. It really consists of parts of three courses: linear algebra, vector statistics, and vector calculus. We will cover these specific topics:
Linear Algebra:
matrix algebra; Gaussian elimination and LU factorization; examples of vector spaces; vector subspaces; linear independence, span and basis; matrix rank; orthogonal projections; least squares approximations; software for linear algebra
Statistics:
descriptive statistics; elementary probability; distributions (continuous and discrete); expected values; unbiased estimators; statistical inference; regression; software for statistics
Vector calculus:
curves and surfaces; vector fields; line and surface integrals; path independence; potential functions and conservative fields; Green's theorem; Stokes' theorem (as time allows); the divergence theorem (as time allows)
For the vector calculus part of the course, our text will be Chapter 14 of University Calculus, by Hass Weir and Thomas. The instructor will supply (at minimal cost, to cover copying) notes for the linear algebra and statistics portions.

Course objectives

Along with these (and every bit as importantly, in my view), I would like to see you grow as mathematics students. Here are some thoughts on that subject.

Software.   There are two software packages with which you are expected to become familiar during the course. Octave is a very good package for doing numerical computations. It has many commands that are identical to Matlab (code written to carry out simple operations in one may often be used without modification in the other), which is one of the main software packages professionals use to do linear algebra-type computations. Calvin has Matlab available both in the mathematics and engineering computer labs, and you are welcome to use it whenever software for linear algebra required. Octave has the advantage of being distributed under a GNU public license, meaning that you can download it to your home computer for free. It is available in Mac OS X, Linux, and Windows versions, so if you get a copy be sure to get one that is appropriate for your machine.

There is another package, which goes by the name R, that is particularly well suited for doing statistical computations. When our focus turns to statistics, we will begin using it instead of Octave/Matlab. You may download R and related material (in particular, manuals) at http://cran.r-project.org/.

Grading.   Your grade will be determined as a weighted average with the following weights

Projects, quizzes and homework     19%
Exams         54% (18% apiece)
Final Exam 27%

Exams.   There will be 3 exams given during the term. The dates are Oct. 4, Nov. 1, and Dec. 6. Rather than trying to sift through the various reasons why an exam must be missed to decide which ones are excused, I have adopted a policy of allowing the final exam to replace your worst exam if, indeed, the grade on the final is better. No make-up exams will be given, and exams may not be taken early.

The final exam is cumulative, and will take place on Thursday, Dec. 13, at 9 am. The college requires that I give you the exam at this time, so schedule your travel plans accordingly.

Homework.   Most weeks homework will be assigned on 4 days, generally in the form of problems. The specifics of a particular problem set are elaborated from the homework page, which you should visit after every class period in order to see what problems may have been added to a set to reinforce the material covered on that day. The due dates for problems sets appear on the course calendar. Problem sets will be collected twice per week, in general, and must be submitted by 3 pm to ensure being on time. Once the grader has taken the class' set, no new submissions will be accepted.

Your write-ups for all assignments must be in your own hand and words, except when otherwise noted. This, however, does not mean you are to work in isolation. Quite to the contrary, I encourage you to come together with other members of the class to form a study group, and schedule regular meetings. I strongly believe that students can earn as much as one letter grade higher by building one another up in this fashion. Read this page for more on why I think participating in a study group is important, my vision of how it might function in order to be of most benefit to all who participate, and what pitfalls one should avoid when working with others so as to maintain personal accountability for the material.

Give as much attention to presenting your solutions in a coherent manner (using mathematical symbols as part of your sentence structure) as you give to actually solving problems, as it is the explanation of each problem that is graded (not simply the answer itself). Submission of work that incorporates another's writeup, even on homework, will be considered academic dishonesty. (See Section 4.2.8 of the Faculty Handbook.) You may borrow someone's idea for solving a problem. When it is the case that this borrowing represents a significant step in your answer, indicate this on your write-up (i.e., give the person's name if a member of the class, the url of the pertinent website, etc.).

Contacting me.   My office is NH 281. If you are having trouble in the course — if you do not understand something important or have some special circumstance that impedes your performance — see me about it right away. Do not put things off. The hours I am intentionally in my office for meeting with students are posted on my homepage, as they are subject to change during the semester. If we cannot hook up at one of these times, feel free to talk with me about an appointed time to meet, or swing by my office and see if I am available to help.

I may be reached by phone at x66856, but a better way to reach me for a non-technical question is by email. If you require my approval for something, do not consider having left a message for me as equivalent to having obtained that approval.

Accomodations.   [an error occurred while processing this directive]


This page maintained by:
Thomas L. Scofield
Department of Mathematics and Statistics
Calvin College

Last Modified: Thursday, 30-Aug-2007 12:04:15 EDT