Office: 109 Altgeld Hall,
Email: jmmackay at illinois dot edu
Calculus is the study of change. In single-variable calculus (i.e., Calculus I and II) you have seen how to study the behavior of quantities that depend only on a single variable. Real life situations are often more complicated. For example, we want to be able to understand how a particle moves in three dimensional space, the flow of air over a wing, or how to optimize profit for a production process that depends on choices of many different parameters. Multi-variable calculus (Calculus III) gives us powerful tools to approach these kind of problems.
In this course we will study limits, differentiation and integration for vector-valued functions and functions of several variables. We will also introduce ideas like vector fields, curves and surfaces in this context. (The picture above gives an example of a bug crawling through a force field. A line integral tells us how much energy this takes. There are more realistic examples.) We'll finish by studying amazing generalizations of the fundamental theorem of calculus into this multi-dimensional world: Green's Theorem, Stokes' Theorem and the Divergence Theorem.
One of the benefits of being in an Honors section is that we have a smaller class size and more time available to discuss the material in class. I expect you to come prepared, having done any recommended work, and to be willing to present your work in class.
Note that, as an Honors section, this class requires departmental approval to register. If you want to register, please go to the Undergraduate Mathematics Office in 313 Altgeld Hall.
There will be weekly homework assignments, collected at the start of class on Wednesday. The first homework assignment will be due the second week of class.
You are free (and encouraged) to work with fellow students on the homework problems.
However, you must write up your final solutions by yourself.
On each assignment write one of the following statements:
Your lowest homework score will be dropped.
There will be three hour long exams in class, and a final. The class exams are set to be on February 23, March 30, and April 27.
The first class exam will cover material through section 2.5. The second class exam will cover material from 2.6 through 5.4. The third class exam will cover material from 5.5 through 7.2.
(Note that this is provisional and may be adjusted as the semester progresses.)
The final will be on Tuesday, May 11, 8:00-11:00 am, and will cover all the material we have seen on the course.
Your grade will be determined as follows:
15% homework, 3 * 15% hour exams, 40% final.
Letter grades will be assigned according to: A-/A/A+ 90%, B-/B/B+ 80%, C-/C/C+ 70%, D/D+ 60%, F for less than 60%. This may be adjusted downwards if necessary.
I reserve the right to give a lower grade in exceptional circumstances, such as failing to complete multiple homework assignments, or missing exams without reason. Cheating may result in a substantially lower grade, or even an F.
If you are ill or otherwise unable to complete an assignment on time, or take an exam, please get a letter from the dean's office (http://www.odos.uiuc.edu/).
To insure that disability-related concerns are properly addressed from the beginning, students with disabilities who require assistance to participate in this class, or alternative exam arrangements, are asked to contact me as soon as possible.
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