Teaching/2017-2

2017-2

Advanced Calculus II (Grading/Teaching)

Instructor: Professor Hyunseok Kim (Grading and Teaching) / Young-Ran Lee (Teaching)
Office Hour: 15:00 ~ 17:00 Tuesday (@Math Tutoring Center) or by appointment
E-mail: willkwon [at] sogang email address

TA Notes

Week 1. Review of Advanced Calculus I
Additional exercises
Week 2. Limit superior and Limit Inferior  / Convergence test
–  Supplementary note (Written partially in Korean)
Week 3. Convergence test / Uniform convergence / Weierstrass approximation theorem
Week 4. Pointwise and uniform convergence / Power series
Supplementary note (space filling curve)
Supplementary note (Local Existence and Uniqueness IVP for ODEs)
Week 5. Uniform convergence, power series, limit points
Week 6. Topology on Euclidean spaces
Week 7. Compactness: history and some examples
Week 8. Topology on Euclidean spaces: problem solving I
Week 9. Topology on Euclidean spaces: problem solving II
Week 10. Relative topology and connected sets
Supplementary note (Topologist sine curve)
Week 11. Differentiation
Supplementary note (Steadty heat equation in a ball)
Week 12. Inverse function theorem and implicit function theorem

Grading policies / Selected Homework Problem Explained:

Homework 1  (09/26)

Chapter 1 Exercise 1.68
Chapter 5. Exercise 5.23, 5.33, 5.45, 5.51; Problem 5.1, 5.4, 5.6

Homework 2  (10/12)
Exercises 5.56, 5.68, 5.74, 5.80
Problems 5.8, 5.9, 5.13, 5.18

Homework 3  (10/26)

Problems 5.22, 5.24, 5.26, 6.2, 6.4
Exercises 6.11, 6.14, 6.23

Homework 4  (11/21)

Exercises 6.29, 6.33, 6.37, 6.40, 6.47, 6.57, 6.59;
Problems 6.7, 6.11, 6.13

Homework 5-6  (12/14)

Exercise 6.76; 7.3, 7.7
Problems 6.20, 6.21, 6.22, 6.25
+ Additional

 

Useful links

수학 글쓰기 (Mathematical Writings)

Teaching at the university level

Mathematical Writings
https://www1.maths.leeds.ac.uk/~khouston/pdf/htwm.pdf

Terry Tao’s advices
https://terrytao.wordpress.com/career-advice/

Writing the Greek Alphabet (Video)

 

Supplementary Readings