分析導論(一)

The purpose of this course is to introduce to our students the basic foundations for the differential and integral calculus. The course will stress the importance of writing rigorous mathematical proofs. So, topics covered will include the concept of limit and that of continuity of a function. The limiting behavior of a sequence or that of a series. Finally, we will give a rigorous treatment of the theory of differential calculus, as well as a self contained theory of Riemann integral.

Calculus I.

There will be no required textbook. However, it is useful to have the following classical book as an important reference: Principle of Mathematical Analysis, by Walter Rudin.

Homework assignments 15% Quiz 5% First mid term 25% Second mid term 25% Final Exam 30% Students taking this course are expected to attend each class. Students are expected to take detailed and careful lecture notes on their own. There will be no official lecture notes provided. It is important to keep in mind that no make-up exam and quiz will be allowed, unless a student can provide solid evidence which supports the excuse (such as accident etc) of missing a particular exam or quiz.

Principle of Mathematical Analysis, by W. Rudin.