KOW Pu Zhao (邱普照)

General Information

• Begins ~ ends: September 12, 2023 ~ January 12, 2024
• Instructor: Pu-Zhao Kow
• Email: pzkow [at] g.nccu.edu.tw
• Office hour: Thursday (16:10 ~ 17:00)
• Teaching Language: Chinese and English
• Lecture Note: Pu-Zhao Kow, Complex analysis. Note: The lecture note may update during the course.
• TA class: Tuesday (15:10 ~ 16:00)

References

• J. Bak and D. Newman, Complex Analysis, Undergraduate Texts in Mathematics, Springer, New York, third edition, 2010. MR2675489, Zbl:1205.30001, doi:10.1007/978-1-4419-7288-0
• E. Freitag and R. Busam, Complex Analysis, Universitext, Springer-Vergag, Berlin, second edition, 2009. MR2513384, Zbl:1167.30001, doi:10.1007/978-3-540-93983-2

Prerequisite

• Calculus

Homeworks

• Homework 1: Return to TA by September 26, 2023 (Tuesday) 16:00
• Homework 2: Return to TA by October 3, 2023 (Tuesday) 16:00
• Homework 3: Return to TA by October 12, 2023 (Thursday) 16:00
• Homework 4: Return to TA by October 17, 2023 (Tuesday) 16:00
• Homework 5: Return to TA by October 24, 2023 (Tuesday) 16:00
• Homework 6: Return to TA by October 31, 2023 (Tuesday) 16:00
• Homework 7: Return to TA by December 5, 2023 (Tuesday) 16:00
• Homework 8: Return to TA by December 12, 2023 (Tuesday) 16:00
• Homework 9: Return to TA by December 19, 2023 (Tuesday) 16:00
• Homework 10: Return to TA by December 26, 2023 (Tuesday) 16:00

Schedule

• The lectures are on Tuesday (14:10-15:00) and Thursday (14:10-16:00) at 志希070221.
• The TA class is on Tuesday (15:10-16:00) at 志希070221.

Time	Room	Activities
12.09.2023 14:10-15:00	志希070221	Week 1 - Lecture (Tuesday): The complex numbers (definition of complex plane)
14.09.2023 14:10-16:00	志希070221	Week 1 - Lecture (Thursday): The complex numbers (sequences in complex plane)
19.09.2023 14:10-15:00	志希070221	Week 2 - Lecture (Tuesday): The complex numbers (open sets in complex plane)
19.09.2023 15:10-16:00	志希070221	Week 2 - TA class (Tuesday)
21.09.2023 14:10-16:00	志希070221	Week 2 - Lecture (Thursday): The complex numbers (continuous functions), Differentiation (complex derivatives and Cauchy-Riemann equation)
26.09.2023 14:10-15:00	志希070221	Week 3 - Lecture (Tuesday): Differentiation (polynomial and power series)
26.09.2023 15:10-16:00	志希070221	Week 3 - TA class (Tuesday): Return Homework 1 to TA before 16:00
28.09.2023 14:10-16:00	志希070221	Week 3 - Lecture (Thursday): Differentiation (power series)
3.10.2023 14:10-15:00	志希070221	Week 4 - Lecture (Tuesday): Exponential, sine and cosine functions
3.10.2023 15:10-16:00	志希070221	Week 4 - TA class (Tuesday): Return Homework 2 to TA before 16:00
5.10.2023 14:10-16:00	志希070221	Week 4 - Lecture (Thursday): Fundamental theorem of line integral, Cauchy closed curve theorem
10.10.2023 14:10-15:00	志希070221	Week 5 - Public holiday (Tuesday)
10.10.2023 15:10-16:00	志希070221	Week 5 - Public holiday (Tuesday)
12.10.2023 14:10-16:00	志希070221	Week 5 - Lecture (Thursday): Cauchy closed curve theorem. Return Homework 3 to TA before 16:00
17.10.2023 14:10-15:00	志希070221	Week 6 - Lecture (Tuesday): Cauchy integral formula
17.10.2023 15:10-16:00	志希070221	Week 6 - TA class (Tuesday): Return Homework 4 to TA before 16:00
19.10.2023 14:10-16:00	志希070221	Week 6 - Lecture (Thursday): Power series and entire function, Liouville theorem
24.10.2023 14:10-15:00	志希070221	Week 7 - Lecture (Tuesday): Local power series and analytic function
24.10.2023 15:10-16:00	志希070221	Week 7 - TA class (Tuesday): Return Homework 5 to TA before 16:00
26.10.2023 14:10-16:00	志希070221	Week 7 - Lecture (Thursday): Local power series and analytic function
31.10.2023 14:10-15:00	志希070221	Week 8 - Lecture (Tuesday): Morera's theorem
31.10.2023 15:10-16:00	志希070221	Week 8 - TA class (Tuesday): Return Homework 6 to TA before 16:00
2.11.2023 14:10-16:00	志希070221	Week 8 - Lecture (Thursday): Morera's theorem
7.11.2023 14:10-15:00	志希070221	Week 9 - Lecture (Tuesday): Review and solving exercises
7.11.2023 15:10-16:00	志希070221	Week 9 - TA class (Tuesday): No homework this week
9.11.2023 14:10-16:00	志希070221	Week 9 - Lecture (Thursday): Review and solving exercises
14.11.2023 14:10-15:00	志希070221	Week 10 - Lecture (Tuesday): Review and solving exercises
14.11.2023 15:10-16:00	志希070221	Week 10 - TA class (Tuesday): No homework this week
16.11.2023 14:10-16:00	研究250201	Week 10 - Midterm exam (Thursday) [Update: November 8, 2023] The venue changed from 志希070221 to 研究250201
21.11.2023 14:10-15:00	志希070221	Week 11 - Lecture (Tuesday): Riemann's principle of removable singularities
21.11.2023 15:10-16:00	志希070221	Week 11 - TA class (Tuesday): No homework this week
23.11.2023 14:10-16:00	志希070221	Week 11 - Lecture (Thursday): Riemann's principle of removable singularities
28.11.2023 14:10-15:00	志希070221	Week 12 - Lecture (Tuesday): Riemann's principle of removable singularities, Laurent expansion
28.11.2023 15:10-16:00	志希070221	Week 12 - TA class (Tuesday): No homework this week
30.11.2023 14:10-16:00	志希070221	Week 12 - Lecture (Thursday): Cauchy's residue theorem
5.12.2023 14:10-15:00	志希070221	Week 13 - Lecture (Tuesday): Some applications in combinatorics (Egorychev method)
5.12.2023 15:10-16:00	志希070221	Week 13 - TA class (Tuesday): Return Homework 7 to TA before 16:00
7.12.2023 14:10-16:00	志希070221	Week 13 - Lecture (Thursday): Some applications in combinatorics (Egorychev method), the analytic function "log z"
12.12.2023 14:10-15:00	志希070221	Week 14 - Lecture (Tuesday): the analytic function "log z", infinite products
12.12.2023 15:10-16:00	志希070221	Week 14 - TA class (Tuesday): Return Homework 8 to TA before 16:00
14.12.2023 14:10-16:00	志希070221	Week 14 - Lecture (Thursday): Infinite products and Weierstrass product theorem
19.12.2023 14:10-15:00	志希070221	Week 15 - Lecture (Tuesday): Infinite products and Weierstrass product theorem
19.12.2023 15:10-16:00	志希070221	Week 15 - TA class (Tuesday): Return Homework 9 to TA before 16:00
21.12.2023 14:10-16:00	志希070221	Week 15 - Lecture (Thursday): The gamma function
26.12.2023 14:10-15:00	志希070221	Week 16 - Lecture (Tuesday): Review
26.12.2023 15:10-16:00	志希070221	Week 16 - TA class (Tuesday): Return Homework 10 to TA before 16:00
28.12.2023 14:10-16:00	志希070221	Week 16 - Lecture (Thursday): Review
2.1.2024 14:10-15:00	志希070221	Week 17 - No class (Tuesday)
2.1.2024 15:10-16:00	志希070221	Week 17 - TA class (Tuesday): No homework this week
4.1.2024 14:10-16:00	志希070221	Week 17 - Final exam (Thursday)
9.1.2024 14:10-16:00	志希070221	Week 18 - No class (Tuesday)
11.1.2024 14:10-16:00	志希070221	Week 18 - Return exam papers (Thursday)

Completion

• The course can be taken for credit by attending the lectures, returning written solutions (60%) and taking taking midterm and final exams (each 20%).