NCHU Course Outline
Course Name (中) 複變函數論(3343)
(Eng.) Functions of Complex Variables
Offering Dept Department of Applied Mathematics
Course Type Required Credits 3 Teacher LI,YUAN-CHUAN
Department Department of Applied Mathematics / Undergraduate Language Chinese Semester 2026-SPRING
Course Description Introduce power series, mobius transformations, analytic functions, theory of complex integration etc.
Prerequisites
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
瞭解複變積分理論、熟用複變積分公式及應用。
1.Basic Knowledge in Mathematical Sciences
2.Professional Knowledge in Mathematical Analysis
20
80
Lecturing
Quiz
Assignment
Other
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 1. Introduce complex numbers, Mobius transformations and curves
Week 2 2. Mobius transformations and curves
Week 3 3. Mobius transformations and curves
Week 4 4. Mobius transformations and curves
Week 5 5. Riemann-Stieltjes integral and derivative
Week 6 6. Riemann-Stieltjes integral and derivative
Week 7 7. Riemann-Stieltjes integral and derivative
Week 8 8. Riemann-Stieltjes integral and derivative
Week 9 9. Riemann-Stieltjes integral and derivative
Week 10 10. Cauchy integral formula, residue theorem and some related results
Week 11 11. Cauchy integral formula, residue theorem and some related results
Week 12 12. Cauchy integral formula, residue theorem and some related results
Week 13 13. Cauchy integral formula, residue theorem and some related results
Week 14 14. Maximum modulus theorem and related results
Week 15 15. Maximum modulus theorem and related results
Week 16 16. 期末考
self-directed
learning		    03.Preparing presentations or reports related to industry and academia.
Evaluation
考試、習題、作業、平時成績
Textbook & other References
參考書：
1. Fundamentals of Complex Analysis 3ed.
Author: E. B. Saff & A. D. Snider (歐亞書局)
2. Complex Variables Author: Levinson/ Redheffer
Teaching Aids & Teacher's Website

Office Hours
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Update Date, year/month/day：2026/01/02 19:16:18 Printed Date, year/month/day：2026 / 4 / 16
The second-hand book website：http://www.myub.com.tw/