Calculus Theory 2

Instructor: John Leo
Course webpage:
Free Periods: 2, 5, 6 in Room 15. Also conference periods and before and after school. It's best to send me email to arrange a time to meet.



The catalog description (which I wrote) says it best:  This course is the second course in a two-year sequence of honors pre-calculus and calculus. The second year covers integration, the fundamental theorem of calculus, infinite series, polar and vector functions, complex functions, and an introduction to differential equations. Compared to the regular BC sequence this course goes into more depth, and concentrates on theoretical aspects as well as applications of calculus. Students will be well-prepared for the BC level AP exam, as well as honors-level college mathematics courses.

The textbook for this class is Calculus by Michael Spivak.  Be sure to get the fourth edition.  Much of the text of the third edition (which is similar, but has some signifcant differences) is available on Google Books.

I've gathered some information about similar courses at colleges, as well as follow-up courses you might pursue.

This year we will cover chapters 13-24 of the textbook, excluding the starred sections, and this will be supplemented by some additional BC material (primarily differential equations).  We'll also spend some time on special topics, concentrating on the theme this year of number theory and factoring.  We'll try to cover chapters 13, 14, 15, 18 and 19 in the Fall, and chapters 20, 22, 23 and 24 in the Spring.  There will be two or more weeks devoted to review for the BC exam.

There will be a problem set due every other Monday, and we will go over the solutions the following Friday.  If there is time left over you can start on the next problem set.  The following Thursday will be devoted entirely to working on the problem set due the next Monday.  You are welcome and encouraged to work together, but I highly recommend trying to work on each problem on your own before you discuss them with your classmates.

I expect homework to take about one hour per class period (so 4 hours a week).  If you find yourself spending too much or too little time on homework, please let me know.  You are of course welcome to spend even more time on the class if you have the time and the material interests you.  I'm happy to help you further explore any topic you like.  The more time and effort you put into this course, the more you will get out of it.

There will be a test after every two chapters.  So expect three tests per semester, plus a final exam.  There will also be a paper due the first semester.  The topic the paper will be how calculus relates to another subject you are interested in


Problem sets are worth 20% of the first semester grade, tests are worth 50% (50/3% each), the paper is worth 10%  and the final exam is worth 20%.  This is subject to change.

Daily homework is not explicitly graded but is the most important component of the class for learning the material well.


Participation is expected of everyone and is not explicitly graded. It will however affect grades in borderline cases. Everyone is expected to take turns presenting solutions, and everyone should participate in discussions.

Laptop Policy

Laptops are normally not allowed in class and must be kept closed.  You do not need to bring them to class normally.  There may be a few classes in which we will use them, and I will let you know in advance if you'll need to bring your laptop.  When laptops are allowed in class, they may only be used for the task specified.


I encourage you to work with fellow students on homework. However you should attempt each problem on your own first, and all write ups must be your own work. For any problems you hand in, you must specify any help you received, whether from another person or persons, a book, a web site, or any other source. No collaboration is allowed on tests, of course.