Math 20860: Honors Calculus IV

Spring `16


Weekly schedule

Last semester's webpage

Instructor: Jeffrey Diller (click for contact info)

Office hours: Wednesdays 5(ish)-6:30 PM in the math bunker and by appointment. Please take advantage also of the help sessions (also held in the math library's math bunker) from 7-9 every evening Sunday through Thursday.

Official Time and place: MWF 11:30-12:20 AM in Pasquerilla 116, Th 3:30-4:20 in Pasquerilla 109.

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. However, I'd especially like to draw your attention to two very good online sources: Linear Algebra Done Wrong by Sergei Treil (deals only with linear algebra), and some very cool online vector calculus notes by Frank Jones (which cover roughly the same material as Shifrin).

What the course covers: I'll devote the first week to the inverse and implicit function theorems, which concern solutions of non-linear systems of equations. The second week, I'll talk about determinants. Possibly I'll spend a week on eigenvalues and eigenvectors, too. After that it's all integration, first on rectangles and other open subsets of R^n, then on parametrized curves and surfaces. We'll see the usual classical integral theorems (Green's, Stokes', Gauss') in dimensions two and three and in particular the fact that they are all variants on the same much more general theorem (generalized Stokes' Theorem). This will require us to become acquainted with the linear algebra and calculus of `differential forms'. We'll deal with applications as time permits.

How you will be evaluated:

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 2/25 and Thursday 4/7; each worth 15%. of your grade.

Final Exam: Monday May 2 from 4:15-6:15 PM in TBA, comprehensive and worth 30% of final grade.