課程介紹
課程總時長| 12小時7分鐘36秒
單元數| 8個章節 24個單元

Brief Description
Mathematical tools are essential in analysis and prediction for a wide range of engineering problems. Engineering mathematics is a post-calculus course for undergraduate students. It extends the discussion to various types of differential equations and advanced topics. Through class lectures, homework assignments, and exams, you will acquire the knowledge on some but not all the equations with engineering interest and be ready to utilize it in engineering problems such as fluid mechanics, solid mechanics, control theory, etc. Furthermore, you should have a good grasp of the physical meaning behind the math and be able to interpret the solution. This is a two-semester series.

Course keywords
vector calculus, Fourier analysis, partial differential equations, complex analysis

Textbook 
Kreyszig, "Advanced Engineering Mathematics", abridged version 10th ed., John Wiley (2018)

Syllabus 
1. Vector calculus 
2. Fourier series and integral 
3. Fourier transform
4. Sturm-Liouville problem 
5. Partial differential equations 
6. Complex analysis

課程章節
第 1 章:Course Introduction
單元 1 - Course Information
14:15
第 2 章:Vector Calculus
單元 1 - Vector Functions (1)
40:12
單元 2 - Vector Functions (2)
19:32
單元 3 - Curve in 3D Space
25:30
單元 4 - Example of 3D curve
46:31
單元 5 - Differential Operators: Intro
03:30
單元 6 - Differential Operators: Gradient
43:13
單元 7 - Differential Operators: Divergence
31:59
單元 8 - Differential Operators: Curl
21:48
單元 9 - Differential Operators: Curl (2)
21:52
單元 10 - Line Integrals
30:04
單元 11 - Line Integrals: Path Independence
44:16
單元 12 - Green's Theorem
52:56
單元 13 - Surface Integrals
52:28
單元 14 - Flux Integrals
34:04
單元 15 - Gauss' Divergence Theorem
31:48
單元 16 - Stokes Theorem
10:00
單元 17 - Stokes Theorem (2)
45:05
第 3 章:Fourier Analysis
單元 1 - Introduction
10:16
單元 2 - Function space, orthogonal basis
53:43
單元 3 - Function space, orthogonal basis (2)
33:41
單元 4 - Convergence of Fourier Series
11:36
單元 5 - Example
31:18
單元 6 - Even and Odd Function
17:59
第 4 章:
第 5 章:
第 6 章:
第 7 章:
第 8 章:
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張敬 教授

> 動力機械工程學系

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流場中渦流(vortex)的運動及動力學,相關工程應用包含再生能源、仿生力學工程等。

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