We will cover multivariable Calculus, follow Spivak's monograph Calculus on Manifolds. The book's prerequisites are a rigorous course in Calculus (i.e. 1a) and a course in linear algebra (i.e 1b). So it is perfect. The course breaks naturally into two parts. In the first part ( first three chapters of Spivak), we develop the theoryof differentiation and Riemann integration in several variables. In a sense, this is just a natural extension of 1a, but with a greater emphasis on the linear algebra that shows up because we are working in several variables. The second part, which will seem more abstract, and is covered in the last two chapters of Spivak is the study of differential forms. These are things which you integrate on curves and surfaces (and, in general, manifolds.) The main point of this part of the course is to prove all variants of Stokes' theorem (the classical Stokes' theorem, Green's theorem, Gauss' divergence theorem, and others) as a single theorem which can be thought of as the fundamental theorem of calculus. Spivak's book, a masterpiece, is famous for its brevity. This will be great for you. It can be read from cover to cover. This course will be a complete success if, at the end, you understand it from cover to cover.There will be eight problem sets, due on Monday at 2 A.M. There will be a midterm and final. The grades will be distributed:Problem sets 40%Midterm 30%Final 30%Course Meeting Time and Location
Monday, Wednesday and Friday
10:00 - 10:55 am
B122 Gates Chemical Laboratory (GCL, Building #26)
Course Instructor Contact Information and Office Hours276 Cahill
I will hold office hours on Thursdays and Sundays 7-8 P.M. in room 326 of the Fairchild Library.
TA Contact Information and Office Hours
Course Schedule and Textbook
Course PoliciesLate work - No late work accepted without permission in advance.
Assignments
Midterm and Final ExamMidterm available here. The password has been emailed to you. If you have any issues accessing the file, please contact Meagan. The midterm is due at 4 pm on Tuesday May 8th. Final exam available here. The password has been emailed to you. If you have any issues accessing the file, please contact Meagan. The final is due at 4 pm on Friday June 15th.
Collaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |