I.Contents：
(1) Convergence in finite dimensional spaces
(2) Metric Spaces
(3) Differentiability on finite dimensional spaces
(4) Integration on finite dimensional spaces
(5) Fundamental Theorems of vector Calculus
II.Course prerequisite：
III.Reference material ( textbook(s) )：
Textbook：William R. Wade, An Introduction to Analysis
Reference：J. E. Marsden, Elementary Classical Analysis
T. M. Apostol, Mathematical Analysis
IV.Grading scheme：
homework：40%
quizzes：30%　　
final：30%
V.Others：
We shall emphasize theoretical proof and analysis. Calculus is basic requirement.