I.Contents：
We will cover every topic in our main textbook by Folland, and also add some additional materials such as the discussion of submanifolds in Chapter 3, a more detailed introduction to the use of differential forms in §5.9, and the evaluation of more special improper integrals in Chapter 7, etc.. Pugh’s text will be used as a supplementary source of course contents and homework problems.
There will be a weekly or biweekly homework assignments, and the TA section will be held biweekly.
II.Course prerequisite：
CalculusLinear Algebra
III.Reference material ( textbook(s) )：
Main text: G. B. Folland, Advanced Calculus, 2002
Reference text: C. C. Pugh, Real Mathematical Analysis
IV.Grading scheme：
Midterm exam. : 30%
Final exam. : 40%
TA section and HW. : 30%
V.Others：