工程數學 IV | NCUx雲端課程

課程形式

線上

課程名稱

工程數學 IV (02030)

課程編號

422

課程期間

2023-02-13 ~

課程類別

自然科學

時數

12 (小時)

修課人數

簡介

Part(I) Functions of a Complex Variable

Chapter 1 Analytical Function

1.1.1 Complex Number

1.1.2 Polar Form of Complex Number

1.2 Continuity

1.3 Cauchy-Riemann Equation

1.4 The Element Complex Function

1.5 Integration in the Complex Plane

1.6 Cauchy Goursat Theorem

1.7 Integration of Functions with Singular Point

Chapter 2 Infinite Series in Complex Plane

2.1 Taylor’s Expansion

2.2 Laurent’s Expansion

2.3 Summary

2.4 Convergent Regions of Infinite Series

Chapter 3 The Theory of Residues

3.1 Residue, Zero, and Singularity

3.2 Residue Theorem and Formulae of Residues

3.3 The Evaluation of Rear Definite Integrals

Chapter 4 Conformal Mapping

4.1 Conformal Mapping by Elementary Functions

4.2 Analytical Function and Conformal Mapping

4.3 The Bilinear Transformation and Schwartz Christoffle Transformation

Chapter 5 Applications

Part(II) Calculus of Variation

Ch1. Extrema of Function of Several Variable

Ch2. Lagrange’s Multiplier

Ch3. The Euler Equation

Ch4. Natural Boundary Condition

Ch5. The Variational Rotation

Ch6. Variation of a Functional in More General Case

Ch7. Hamilton’s Principle and Lagrange Equation

Part (III) Numerical Methods in General

Ch1. Solution of Equations by Iteration

Ch2. Numerical Integration

Ch3. Methods for 1 st Order Differential Equation

Ch4. Solving Time Dependent PDEs by RK4

任課教授

李顯智老師
Email : hinchili@ncu.edu.tw
分機：03-4227151轉34105

相關連結 : 國立中央大學土木工程系

報名資訊

報名期間

開始: 2023-02-10

總人數限制

無限制

報名費用

其他資訊

承辦人

蔡振瑋 / 教學發展中心 (電子郵件: dwtsai@ncu.edu.tw, 電話: 57137)

鄭雅軒 / 教學發展中心 (電子郵件: yahsuan@ncu.edu.tw, 電話: 57138)

開課單位

NCUx線上課程

課程 QR code

https://ocw.ncu.edu.tw/course/422

課程教材

1.
課程介紹
1. 1.1
  11:14
  
  NCUOCW-工程數學IV- Introduction
2.
第一單元
1. 2.1
  14:47
  
  NCUOCW-工程數學IV-1.1.1 Complex Number
2. 2.2
  26:02
  
  NCUOCW-工程數學IV-1.1.2 Polar Form of Complex Number
3. 2.3
  30:02
  
  NCUOCW-工程數學IV-1.2 Continuity
4. 2.4
  41:22
  
  NCUOCW-工程數學IV-1.3 Cauchy-Riemann Equation
5. 2.5
  06:37
  
  NCUOCW-工程數學IV-1.4 The Element Complex Functions 中文版
6. 2.6
  09:06
  
  NCUOCW-工程數學IV Engineering Math IV-1.4 The Element Complex Functions English Version
7. 2.7
  16:37
  
  NCUOCW-工程數學IV-1.5 Integration in the Complex Plane 中文版
8. 2.8
  24:45
  
  NCUOCW-工程數學IV Engineering Math IV-1.5 Integration in the Complex Plane English Version
9. 2.9
  11:02
  
  NCUOCW-工程數學IV-1.6 Cauchy Goursat Theorem 中文版
10. 2.10
  18:32
  
  NCUOCW-工程數學IV Engineering Math IV-1.6 Cauchy Goursat Theorem English Version
11. 2.11
  20:24
  
  NCUOCW-工程數學IV-1.7 Integration of Functions with Singular Points 中文版
12. 2.12
  30:24
  
  NCUOCW-Engineering Math IV-1.7 Integration of Functions with Singular Points English Version
3.
第二單元
1. 3.1
  08:34
  
  NCUOCW-工程數學IV-2.1 Taylor's Expansion 中文版
2. 3.2
  12:51
  
  NCUOCW-Engineering Math IV-2.1 Taylor's Expansion English Version
3. 3.3
  22:44
  
  NCUOCW-工程數學IV-2.2 Laurent's Expansion
4. 3.4
  07:59
  
  NCUOCW-工程數學IV-2.3 Summary
5. 3.5
  28:29
  
  NCUOCW-工程數學IV-2.4 Convergent Regions of Infinite Series
4.
第三單元
1. 4.1
  17:11
  
  NCUOCW-工程數學IV-3.1 Residue, Zero, and Singularity
2. 4.2
  16:04
  
  NCUOCW-工程數學IV-3.2 Residue Theorem and Formulae of Residues
3. 4.3
  44:12
  
  NCUOCW-工程數學IV-3.3 The Evaluation of Rear Definite Integrals
5.
第四單元
1. 5.1
  14:53
  
  NCUOCW-工程數學IV-4.1 Conformal Mapping
2. 5.2
  11:33
  
  NCUOCW-工程數學IV-4.2 Analytical Function and Conformal Mapping
3. 5.3
  20:27
  
  NCUOCW-工程數學IV-4.3 The Bilinear Transformation and Schwartz Christoffle Transformation
6.
第五單元
1. 6.1
  19:01
  
  NCUOCW-工程數學IV-5 Applications
7.
Part II
1. 7.1
  31:14
  
  NCUOCW-工程數學IV-(II) Ch1 Extrema of Function of Several Variable
2. 7.2
  22:19
  
  NCUOCW-工程數學IV-(II) Ch2 Lagrange's Multiplier
3. 7.3
  31:24
  
  NCUOCW-工程數學IV-(II) Ch3 The Euler Equation
4. 7.4
  18:08
  
  NCUOCW-工程數學IV-(II) Ch4 Natural Boundary Conditon
5. 7.5
  19:37
  
  NCUOCW-工程數學IV-(II) Ch5 The Variational Rotation
6. 7.6
  22:46
  
  NCUOCW-工程數學IV-(II) Ch6 Variation of a Functional in More General Case
7. 7.7
  22:18
  
  NCUOCW-工程數學IV-(II) Ch7 Hamilton's Principle and Langrange Eq
8.
Part III
1. 8.1
  29:40
  
  NCUOCW-工程數學IV-(III) Ch1 Solution of Equations by Interation
2. 8.2
  08:40
  
  NCUOCW-工程數學IV-(III) Ch2 Numerical Integration
3. 8.3
  34:23
  
  NCUOCW-工程數學IV-(III) Ch3 Methods for 1st Order Diff Eqs
4. 8.4
  56:01
  
  NCUOCW-工程數學IV-(III) Ch4 Solving Time Dependent PDEs by RK4

課程資訊

課程資訊