Math 20850: Honors Calculus III

Fall `13

Weekly schedule

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:

    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.