## 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 **