Syllabus for Advanced Calculus

Course purpose

Just as Calc I isn't nearly enough to finish up single variable calculus, Calc III really isn't enough to finish up multi-variable calculus. Thus, in this course we will:

Finish Calculus III Specifically, we'll fully cover the major theorems of vector integration such as Green's theorem, Stoke's theorem, and the divergence theorem.
Motivate our knowledge with physics Much of vector calculus developed out of electrostatics and a deep knowledge of the two goes hand in hand.
Work in various coordinate systems Many of the problems we face will be naturally expressed in the spherical coordinate system. We'll work there enough that it might even start to seem natural.
Explore some other fun topics We'll explore some other fun topics such as surface parametrization and map projection.

Materials

Texts: We'll start the semester in a standard, open calculus text - namely, David Guichard's Community Calculus:
- PDF
- HTML
After a few weeks, we'll transition to H. M. Schey's fabulus div, grad, curl, and all that.
Computer tools: We'll be using the computer for a few things this semester.
- Visualization: We'll be working in 3D and it's nice to be able to visualize the objects we're exploring. I'll put some things right on our web pages but you'll want to be able to generate some of your own images as well. A couple of tools worth trying are:
  - Mathematica While this might seem overkill, it generates some pretty spectacular images and you might as well use it while you've got a site license. Just follow this download link and use your UNCA email address to get your copy.
  - math3d.org A brand new open source tool. We'll find out how good it is.
- Discussion: I've set up a discussion forum for this class. This is mostly just a resource for you to talk about vector calculus with me and amongst yourselves. There will be a few required questions to get you started, though.
- LaTeX: Several homeworks will need to be typed up. LaTeX is the way to go! If you don't already have a copy, you can download it free for Mac or for PC.

Grades

Homework: We'll have several 10-20 point homework assignments that you'll need to type up.
Discussion forum: Several individualized assigments will be assessed via our discussion forum.
Quizzes: There will be two quizzes during the semester worth about 40 points apiece. Likely dates for those quizzes are:
- Tuesday, February 13
- Tuesday, March 27
Exams: There will be two exams during the semester worth about 100 points apiece. Likely dates for the exams are:
- Tuesday, February 27
- Tuesday, April 10
Final exam: There will be a comprehensive, final exam worth around 180 points at 11:30 AM on Thursday, May 3.
Final grades: I will determine final grades using a scale not more stringent than the standard 90-80-70-60 scale. You will be apprised of your standing as the term progresses.
Late work: In general, I don't accept late work.

Your rights and responsibilities

It's worth understanding your rights and responsibilities as a student at UNCA. One of my responsibilities is to make sure you have the information that you need to do that. Since this is common to all classes, I've got that information on this legalese document.