Course Name	Analysis II
Credits	3
Professor(s)	Name	Yeol Je Cho
	Department	Department of Mathematics Education

COURSE DESCRIPTION

Course Objectives

It is to give the following topics :

(1) Continuous functions in metric spaces

(2) Compact and connected spaces

(3) Riemann-stieltjes integrals

(4) Pointwise and uniform convergences

(5) Power series

(6) Normed liaean spaces and inner product spaces

MAIN TEXTBOOK and FURTHER READINGS

Main Textbook: Yeol Je Cho dt al., Foundation of Real Analysis (2005).

Further Reading:

- K. A. Ross, Elementary Analysis the Theory of Calculus.

- W. Rudin, Principles of Mathematical Analysis.

ASSIGNMENTS AND GRADING

Assignments: Solutions of Exercises of each section

Grading Scheme: Attendance (10%), Mid-term Exam (30%), Final Exam (40%), Tasks (20%)

COURSE SCHEDULE

Course Outline

Week 1 : Continuous functions in metric spaces.

Week 2 : Compact spaces.

Week 3 : Connected spaces and complete metric spaces.

Week 4 : Derivatives of function in the real line.

Week 5 : Mean Valve Theorem and Taylor's Theorem.

Week 6 : Riemann-Stieltjes integrals.

Week 7 : Functions of bounded variation.

Week 8 : Mid-term Exam.

Week 9 : Pointwise and uniform convergence.

Week 10 : Series of functions and power series.

Week 11 : Limit Theorem of Abel and Tauber's Theorem.

Week 12 : Transendental functions.

Week 13 : Normal linear spaces and inner product spaces.

Week 14 : Fourier series.

Week 15 : Final Exam.

CONTACT DETAILS

Tel.: +82 55 751 5673

e-mail : yjcho@gsnu.ac.kr