Math 20850: Honors Calculus III

Fall `15


Weekly schedule

Instructor: Jeffrey Diller (click for contact info)

Office hours: 5-6:30 PM Wednesdays (my office or, most likely, across the hall in HH 125) and Thursdays following tutorial 4:20-5:00 in HH 117. There will also be regular help available, 7-9 PM Sun-Thurs in the “Math Bunker” (partitioned off space in the math library) for all freshman/sophomore honors math courses. One or more upperclass honors math majors will be available then to discuss homework problems and other issues concerning these classes.

Official Time and place: MWF 11:30-12:20 AM in Hayes-Healy 127, and Th 3:30-4:20 PM in Hayes-Healy 117.

Textbook: Multivariable Mathematics by Theodore Shifrin. There are also some very cool online vector calculus notes by Frank Jones, which I might occasionally use as a source, particularly for homework problems. For linear algebra topics, there is an online book Linear Algebra Done Wrong (no kidding) by Sergei Treil that is a good alternative reference.

What the course covers: This class is the first semester in a two semester sequence that combines linear algebra and multivariable calculus. In the first semester we'll cover most of the linear algebra and most of the calculus associated with differentiation. Whatever is left over will be covered along with integration in the second semester. In terms of the textbook, we will certainly cover chapters 1-4 this semester, then move on to chapters 5,6,9 (not necessarily in that order) at the end of this semester and the beginning of next, and finish the year with chapters 7 and 8.

Throughout, I plan to emphasize all sides of the material: computational, intuitive, and logical. This means in particular that I will not only state, but prove most facts that I present, and I will expect you to: remember and reproduce precise definitions of key concepts and statements of important theorems; invent and (nicely) write down correct proofs of more elementary facts; and give specific counterexamples to false statements.

What the course is about: Most worthwhile uses of mathematics (both inside math and in applications to other fields), require one to deal with functions that involve more just one variable. For instance, describing the weather in South Bend, IN involves quantities including temperature, humidity, windspeed and direction, precipitation; and actually predicting the weather requires understanding the relationships among these variables and many others. Calculus is an important tool in this enterprise. You might imagine that multi-variable calculus is just a subscripted rehash one variable calculus, but there are two important differences.

First of all, if you're like most people, you get confused pretty quickly when trying to keep track of many things at once. Linear algebra is a mathematical 'organizing' tool that was developed to allow us to talk about many variable situations without going completely crazy. In particular many facts in multivariable calculus are much easier to state and comprehend using the language of linear algebra. Second, from a visual point of view, more variables means more dimensions, and as soon as there's more than one dimension, thinking geometrically becomes important. Hence multivariable calculus tends to have an even more geometric feel than its one variable predecessor.

How you will be evaluated:

Quizzes: beginning of class each Thursday (except 8/27), worth a maximum of 10% of your grade. These are just to make sure you're keeping up with the material and will consist of a simple problem from the current week's homework and writing down the statement of a definition or theorem, etc, from the previous week. If the class is doing consistently well on these, thus reassuring me, I might stop giving them.

Homework: assigned and collected each Friday, together with quizzes worth 40% of your grade. Homework is the most important part of this course. I urge you to start each assignment the day after I post it, and to take a lot of care in writing up your solutions. I strongly encourage you to work on homework with other students, and you are welcome to turn in joint homework solutions with up to two other students in the class. Collaborating with other people is an important skill in mathematics and also tends to make it all more fun. There is one exception to this: occasionally I give out extra credit problems. On these, I expect you to work alone and turn solutions in to me apart from other homework.

Two in-class midterm Exams: Thursday 10/8 and Thursday 11/19; each worth 15%. of your grade.

Final Exam: Monday, December 14 from 4:15-6:15 in 127 Hayes-Healy. comprehensive and worth 30% of final grade.