CO2013: Engineering Mathematics –
Complex Analysis, Fall 2024
Instructor
Prof. Dah-Chung
Chang, E-mail: dcchang@ce.ncu.edu.tw
Office: E1-311, TEL: 03-4227151 ext. 35511
Lecture Time
Wed. 1:00-1:50pm, Thur. 1:00-2:50pm
TA Information
Office: E1-306, TEL: 03-4227151 ext. 35534
** 順利通過複變課程的三個步驟:
1. 上課用心聽講作記錄, 弄清楚講義觀念與熟悉重點定理。
2. 課後做課本相關單元例題與勾選的練習題。
3. 細心練習歷屆考古題, 掌握考試題型與磨練臨場解題。
** 祝大家學習愉快!
Course Outline
1.
Complex Analytic
Functions
1-1 Complex Number
Video Part-2 (錯誤注意: page 22, time 20:22 處, √5 應修正為 √13。)
HW#1
(Textbook Exercises)
1.2:
13, 14, 15, 16
1.3:
4, 5, 7, 12
1.4:
1, 2, 3, 4, 5, 12, 20, 21, 23
1.5: 4,
5, 7, 9, 10, 11, 14, 15, 16 17
1.6:
2, 3, 4, 5, 6, 7, 8
1.7: 1
1-2 Complex Analytic
Functions
2.1:
1, 2, 4
2.2:
7, 8, 9, 11, 14, 15, 21, 25
2.3:
4, 9, 10, 11, 14, 15
2.4:
1, 2, 3, 5, 6, 12
2.5:
3, 6, 10, 12, 18, 22
1-3 Complex
Elementary Functions
HW#2
(Textbook Exercises)
3.1:
3, 5, 11, 13, 15, 17
3.2:
1, 4, 5, 8, 10, 11, 12, 16, 17
3.3:
1, 3, 4, 5
3.5:
1, 3, 5, 6, 7, 8, 10
<Exam-1: occupying 30% of Final Grade
>
2.
Complex
Integration
4.1:
1, 7, 8, 9, 10, 11
4.2:
5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17
4.3:
1, 2, 4
4.4:
10, 13, 15, 16, 17, 18, 20
4.5:
1, 3, 4, 5, 6, 7, 8, 10
4.6:
1, 2, 4, 5, 18
3.
Complex Series
HW#3
(Textbook Exercises)
5.1:
1, 2, 3, 4, 5, 7, 10, 11, 16
5.2:
1, 4, 6, 11, 13
5.3:
2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 18
5.5:
1, 3, 5, 7, 9
<Exam-2: occupying 30% of Final
Grade>
4.
Residue
Integration
HW#4
(Textbook Exercises)
5.6:
1, 2, 12
6.1:
1, 3, 6, 7
6.2:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
6.3:
1, 2, 3, 4, 5, 6, 7, 8, 11, 14, 15, 16, 17, 18, 19
6.4:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
6.5:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
6.6:
1, 2, 3, 4, 5, 6, 7, 8
6.7:
1, 2, 3, 4, 6, 7, 8, 9, 10, 11
8.2:
1, 2, 3, 5 ,6
8.3:
1, 3 ,4 ,5 ,6
<Exam-3: occupying 40% of Final Grade
>
5.
Conformal Mapping
7.3:
2, 3, 7, 8, 9
7.4:
1, 2
Course Schedule
|
Week |
Day |
Topics |
Remark |
|
1 |
Polar Form, Euler Equation, Powers and Roots of Complex
Numbers |
|
|
|
2 |
Complex Analytic Functions, Cauchy-Riemann Equations,
Harmonic Conjugate |
|
|
|
3 |
10/16-17 |
Complex Elemetary Functions |
|
|
4 |
10/16-17 |
Contour Integral, ML Inequality |
|
|
5 |
10/23-24 |
Cauchy Integral Theorem |
Exam
#1: Unit
1 |
|
6 |
Deformation of Contour, Cauchy Integral Formula |
||
|
7 |
11/6-7 |
Cauchy Integral Formula for Derivative, Cauchy
Inequality, Convergent Series, Comparison Test |
|
|
8 |
Ratio Test, Root Test, |
|
|
|
9 |
Power Series, Radius of Convergence, Operation of Power
Series, Taylor’s Theorem |
|
|
|
10 |
School Sports Days Break |
|
|
|
11 |
Theoretical and Substitution Methods for Taylor’s
Series, Laurent Series |
|
|
|
12 |
Laurent Series, Singularity, Orders of Zeros and Poles |
||
|
13 |
12/12 |
Residue, Cauchy’s Residue Theorem |
Exam
#2: Unit 2-3 |
|
14 |
Cauchy’s Residue Theorem , Trigonometric Integration,
Improper Integral, Jordan’s Lemma |
|
|
|
15 |
Fourier Integrals, Integral of Indented Contour,
Integration Along a Branch Cut, Summing Infinite Series, Argument Principle, Rouche’s Theorem |
|
|
|
16 |
Laplace and Inverse Laplace Transform, Fourier and
Inverse Fourier Transform |
||
|
17 |
1/9 |
Exam #3 |
Exam #2: Unit 4 |
LectureNotes
Unit-1:
Unit 1-1 2pp Unit 1-2 2pp Unit 1-3 2pp
Unit 1-1 1pp Unit 1-2 1pp Unit 1-3 1pp
Examination
in 2024 Class
Exam-3 Solution
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Examination
in 2016 |
Examination
in 2018 |
Examination
in 2019 |
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Examination
in 2020 |
Examination
in 2021 |
Examination
in 2022 |
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Examination
in 2023 |
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Course Material
Textbook:
E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis:
Engineering, Science, and Mathematics, 3rd Edition, 2014. (ISBN: 978-1-292-02375-5,
滄海書局代理)
References
1.
J. H. Mathew and R. W. Howell, Complex
Analysis for Mathematics and Engineering, 6th ed. 2012. (ISBN-13:
978-1449604455, 滄海書局代理)
2. E. Kreyszig,
Advanced Engineering Mathematics, 10th ed., 2011, Chapters 13-17.
(ISBN: 978-0-470-64613-7, 滄海書局代理)
3. J. W. Brown and R. V. Churchill, Complex
Variables and Applications, 9th ed., 2014. (ISBN: 978-1-259-07277-2, 新月圖書代理)
Grading
Policy: Exam-1,2*60%+Exam-3*40%
Grading Report