查詢教學大綱與進度

教學大綱與進度

課程基本資料：

學年期課號課程名稱階段學分時數修教師班級人撤備註

111-2 317034 複變函數 1 3.0 3 ★ 廖天豪電機四甲
電機四乙
電機四丙 0 0 1週【停開】

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
111-2	317034	複變函數	1	3.0	3	★	廖天豪	電機四甲電機四乙電機四丙	0	0	1週【停開】

教學大綱與進度：

教師姓名廖天豪　教師諮商時間(Office Hours)

Email thliao@ntut.edu.tw

最後更新時間 2023-02-12 17:18:30

課程大綱 This course offers complex variables knowledge for engineering application. It covers following topics. 1.Complex Numbers 2.Complex Functions 3.Harmonic Functions 4.Complex Integration 5.Cauchy Theory of Integration 6.Complex Power Series 7.Laurent Series,Residues 8.Conformal Mapping

課程進度Ｗeek 1 Complex Numbers and Their Geometric Representation & Polar Form of Complex Numbers. Powers and Roots Ｗeek 2 Derivative. Analytic Function & Cauchy–Riemann Equations. Laplace’s Equation Ｗeek 3 Exponential Function & Trigonometric and Hyperbolic Functions. Euler’ s Formula Ｗeek 4 Logarithm. General Power. Principal Value & Line Integral in the Complex Plane Ｗeek 5 Cauchy’ s Integral Theorem & Cauchy’ s Integral Formula Ｗeek 6 Derivatives of Analytic Functions & Sequences, Series, Convergence Tests Ｗeek 7 Power Series & Functions Given by Power Series Ｗeek 8 Taylor and Maclaurin Series & Uniform Convergence. Optional Ｗeek 9 Mid-term Ｗeek 10 Laurent Series & Singularities and Zeros. Infinity Ｗeek 11 Residue Integration Method & Residue Integration of Real Integrals Ｗeek 12 Geometry of Analytic Functions: Conformal Mapping & Linear Fractional Transformations (Möbius Transformations) Ｗeek 13 Special Linear Fractional Transformations & Conformal Mapping by Other Functions Ｗeek 14 Riemann Surfaces. Optional & Electrostatic Fields Ｗeek 15 Use of Conformal Mapping. Modeling & Heat Problems Ｗeek 16 Fluid Flow & Poisson’ s Integral Formula for Potentials Ｗeek 17 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem Ｗeek 18 Final

評量方式與標準 1. Homework(50%) 2. Exam (50%)

使用教材、參考書目或其他 【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】

使用外文原文書：是
E. Kreyszig, H. Kreyszig, and E. J. Norminton, Advanced Engineering Mathematics, Tenth. Hoboken, NJ: Wiley, 2011. CHAPTER 13 Complex Numbers and Functions. Complex Differentiation CHAPTER 14 Complex Integration CHAPTER 15 Power Series, Taylor Series CHAPTER 16 Laurent Series. Residue Integration CHAPTER 17 Conformal Mapping CHAPTER 18 Complex Analysis and Potential Theory

課程諮詢管道 Office hour:email thliao@ntut.edu.tw
Office location:綜科213A

課程對應SDGs指標

備註
如需遠距教學開學後提供線上課堂連結

教師姓名	廖天豪　教師諮商時間(Office Hours)
Email	thliao@ntut.edu.tw
最後更新時間	2023-02-12 17:18:30
課程大綱	This course offers complex variables knowledge for engineering application. It covers following topics. 1.Complex Numbers 2.Complex Functions 3.Harmonic Functions 4.Complex Integration 5.Cauchy Theory of Integration 6.Complex Power Series 7.Laurent Series,Residues 8.Conformal Mapping
課程進度	Ｗeek 1 Complex Numbers and Their Geometric Representation & Polar Form of Complex Numbers. Powers and Roots Ｗeek 2 Derivative. Analytic Function & Cauchy–Riemann Equations. Laplace’s Equation Ｗeek 3 Exponential Function & Trigonometric and Hyperbolic Functions. Euler’ s Formula Ｗeek 4 Logarithm. General Power. Principal Value & Line Integral in the Complex Plane Ｗeek 5 Cauchy’ s Integral Theorem & Cauchy’ s Integral Formula Ｗeek 6 Derivatives of Analytic Functions & Sequences, Series, Convergence Tests Ｗeek 7 Power Series & Functions Given by Power Series Ｗeek 8 Taylor and Maclaurin Series & Uniform Convergence. Optional Ｗeek 9 Mid-term Ｗeek 10 Laurent Series & Singularities and Zeros. Infinity Ｗeek 11 Residue Integration Method & Residue Integration of Real Integrals Ｗeek 12 Geometry of Analytic Functions: Conformal Mapping & Linear Fractional Transformations (Möbius Transformations) Ｗeek 13 Special Linear Fractional Transformations & Conformal Mapping by Other Functions Ｗeek 14 Riemann Surfaces. Optional & Electrostatic Fields Ｗeek 15 Use of Conformal Mapping. Modeling & Heat Problems Ｗeek 16 Fluid Flow & Poisson’ s Integral Formula for Potentials Ｗeek 17 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem Ｗeek 18 Final
評量方式與標準	1. Homework(50%) 2. Exam (50%)
使用教材、參考書目或其他	【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】使用外文原文書：是 E. Kreyszig, H. Kreyszig, and E. J. Norminton, Advanced Engineering Mathematics, Tenth. Hoboken, NJ: Wiley, 2011. CHAPTER 13 Complex Numbers and Functions. Complex Differentiation CHAPTER 14 Complex Integration CHAPTER 15 Power Series, Taylor Series CHAPTER 16 Laurent Series. Residue Integration CHAPTER 17 Conformal Mapping CHAPTER 18 Complex Analysis and Potential Theory
課程諮詢管道	Office hour:email thliao@ntut.edu.tw Office location:綜科213A
課程對應SDGs指標
備註	如需遠距教學開學後提供線上課堂連結