Math 20850: Honors Calculus III

Fall `14


Weekly schedule

Instructor: Jeffrey Diller (click for contact info)

Office hours: Wednesdays 5-6:30 PM in the partitioned off space in the math library, Thursdays 4:20-5:20 in DeBartolo 125, and by appointment. Additionally, our graders will hold their own office hours in the partitioned off area of the math library (basement of Hayes-Healy): Jack Burkhart on Mondays (except 9/1) from 9-10 PM and Austin Rodgers on Tuesdays from 5-7 PM.

Official Time and place: MWF 11:30-12:20 AM in Debartolo 317, and Th 3:30-4:20 PM in DeBartolo 125.

Textbook: Multivariable Mathematics by Theodore Shifrin. I put a few other textbooks on reserve in the math library, and you might look at these for alternative explanations/more examples, etc. 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.

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: at the end of class each Wed beginning of class each Thursday, 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: Monday October 6 and Monday, November 24; each worth 15%. of your grade.

Final Exam: Thursday, December 18 from 4:15-6:15 in 317 DeBartolo. comprehensive and worth 30% of final grade.