Math 350: Multivariate Calculus
Winter 2012 / 0900-0950 MTRF / Stanley 045

Mic Jackson, D208, 765-983-1620, micj@earlham.edu
Office Hours: 1000-1150 TR

Content

We will study the basic operations of vector calculus and extend the derivative and the integral which you studied during your first year of calculus to functions of two or more variables, in other words to 3 or more dimensions. The climax of the course comes near the end when we take a brief look at three higher-dimensional analogs of the Fundamental Theorem of Calculus.

Procedures

Each class will begin promptly at 9:00 with a moment of silence. We will start with a few minutes for you to ask questions about that day's reading and/or the current homework assignment. Most days, I will take the majority of time to lecture on new material, discussing important concepts and working example problems related to those concepts. My lectures will relate to the material in the text, but will not be a rehash.

Mathematics is best learned by doing individually and discussing ideas and questions with other students. The relative usefulness of individual versus group work varies among mathematicians. Hilbert, the greatest mathematician of the 19th century, was unable to learn new mathematics independently, but had to work with students or colleagues. However, once he had learned the fundamentals, he was able to go on to a superior mastery of any mathematical topic. Wiles, who proved Fermat's Last Theorem late in the 20th century, worked independently and secretively on that proof over decades, but made extensive use of the work of other mathematicians around the world. A comment commonly made by notable mathematicians is that they have only "stood on the shoulders of giants".

A common mistake of young mathematicians is assuming that the only way to truly master mathematics is to work independently. Another common mistake is to rely too extensively on the hard work of others. A more modern sort of error has to do with use of technological tools. Some students think that a computer algebra system, such as Maple or SAGE, will teach them difficult mathematics. Others are averse to using technology more sophicated than paper-and-pencil. In both cases, the "middle way" is the better way.

Materials and Tools

• Multivariable Concepts and Contexts, 4E, by Stewart
• The author's website. There are some very nice tutorials available through this link.
• Maple (on all lab machines) and the open-source (free) SAGE computer algebra systems provide useful computational and graphical capabilities. I will make extensive use of SAGE for this course, and will provide you with a number of SAGE-based handouts. I strongly encourage you to download SAGE and install it on your computer.
• Three-ring notebook with regular and graphing paper. I have LOTS of once-used paper freely available to you for notes and homework.
• straight-edge and colored pencils

Evaluation

Your course grade will be based on your performance on weekly homework and 3 tests. Each test will include an in-class and a take-home portion.

You will be assigned homework from each section; I will grade a subset of those to provide feedback to you. I expect your homework to be well-organized and self-contained, including the problem statement for each exercise and all relevant work shown in detail. I expect you to hand in final, not first, drafts. I will collect homework at the beginning of class each Monday and return it to you as soon as possible.

Tests will be given as shown on the schedule. The in-class portion of each test will examine your understanding of vocabulary and concepts and your ability to carry out basic computations, and perhaps simple proofs. The take-home portion of each test will involve problems or proofs that require more consideration and time.

Your grade for the course will be based on the average of the letter grades earned on the tests and weekly homework assignments. Each weekly homework has a weight of 1 unit, and each test has a weight of 4 units.

Because different groups of students tend to have somewhat unpredictable difficulties with various parts of this course, I've arranged this schedule so that we have a fair number of "flex" meetings, especially toward the end. Past experience persuades me that we'll need to make use of every one of those open slots, so don't assume they represent free time. Tests will be given as scheduled, regardless of other adjustments we have to make.

Tentative Schedule