Instructor: Jeffrey Diller (click for contact info, general policies, etc.)
Office Hours: by appt (for now at least)
Official Time and place: MWF 10:30-11:20 AM, DBRT 117. Also tutorials every Thursday from 12:30-1:20 In HH 127.
Textbook: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach (4th edition) by Hubbard and Hubbard.
A couple of other sources I plan to rely on are
Calculus volumes 1 and 2, by Apostol
Some really cool Online vector calculus notes by Frank Jones. In particular there are a lot of good problems in these notes.
What we'll cover: This class is the first semester in a two semester sequence. My plan for this semester is to begin by discussing points, vectors and continuity in R^n, culminating in (among other things) a proof of the fundamental theorem of algebra. Then I'll spend some time talking about first order ordinary differential equations. Finally, I'll move on to the main topic for the semester: differentiable functions and mappings on R^n. After working through the definition and basic properties of the derivative of a mapping, we'll cover the chain rule, the inverse and implicit function theorems, higher order partial derivatives and finding and classifying extrema of functions of many variables.
In the second semester, I plan to (if necessary) finish the syllabus from the first semester and move on to the theory of integration. Time permitting, I'll cover additional topics: e.g. autonomous systems of differential equations, applications to the theory of electromagnetism, and curvature of surfaces.
Important Remark: It's tempting to imagine that calculus for functions of several variables is just a subscripted rehash of calculus for functions of a single variable, which you're no doubt quite familiar with by now. This is far from true, however, as extra dimensions means that geometry becomes the main character, and linear algebra becomes the language used on stage. Few things worth modeling in the world can be described well by only one variable, but when the variables outnumber the modeler (i.e. you) the situation calls for a whole new mathematical strategy.
How you will be evaluated:
Homework: assigned and collected every Friday, worth 50% of your final grade. I highly encourage you to work together on homework assignments, but I expect you to write up solutions yourself. No copying allowed! Occasionally I give out extra credit problems. On these, I expect you to work alone.
Midterm Exam: 10/18 in class, worth 20% of final grade. Possibly with take home problems passed out in advance and due at exam time.
Final Exam: Tuesday Dec 17 from 4:15-6:15. in Debartolo 117 (our MWF classroom) comprehensive and worth 30% of final grade. Possibly a take home portion, too.
Paper: over the course of the year you'll be required to write a paper of at least 10 pages. A paper will be required for the honors algebra sequence, too, and you can count the same paper toward both honors classes. It won't be due til the 2nd half (tentatively April 9) of the 2nd semester, but you'll be required to consult with me and then settle on a topic and sources to consult by Dec 1. I'll count that preliminary effort toward your last hwk assignment this term. If you're a math major you can also enter the paper in the department's annual Taliaffero competition (same deadline). More on this later...