11320 工程數學二

# Required Courses # Undergraduate Program
7 Lectures / 61 Sections / 35h 43m 44s
Lecture 1：Course Introduction
Section 1
14:15
Lecture 2：Vector Calculus
Section 1
40:12
Section 2
19:32
Section 3
25:30
Section 4
46:31
Section 5
03:30
Section 6
43:13
Section 7
31:59
Section 8
21:48
Section 9
21:52
Section 10
30:04
Section 11
44:16
Section 12
52:56
Section 13
52:28
Section 14
34:04
Section 15
31:48
Section 16
10:00
Section 17
45:05
Lecture 3：Fourier Analysis
Section 1
10:16
Section 2
53:43
Section 3
33:41
Section 4
11:36
Section 5
31:18
Section 6
17:59
Section 7
24:37
Section 8
24:39
Section 9
24:48
Section 10
57:19
Section 11
27:06
Section 12
14:10
Section 13
09:22
Section 14
51:21
Section 15
15:16
Section 16
43:43
Section 17
49:04
Lecture 4：Sturm-Liouville Problem (Theory)
Section 1
53:53
Section 2
52:20
Section 3
49:46
Lecture 5：Partial Differential Equations
Section 1
23:30
Section 2
24:48
Section 3
53:47
Section 4
48:06
Section 5
31:08
Lecture 6：Heat Equation
Section 1
23:58
Section 2
44:52
Section 3
49:51
Section 4
50:31
Section 5
52:40
Section 6
28:35
Section 7
51:51
Section 8
55:23
Section 9
47:18
Lecture 7：Complex Analysis
Section 1
30:58
Section 2
23:44
Section 3
54:41
Section 4
22:20
Section 5
52:00
Section 6
41:56
Section 7
18:29
Section 8
30:55
Section 9
57:23
Introduction
Duration｜ 35h 43m 44s
Total Lectures｜ 7 Lectures 61 Sections

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

Lectures
Lecture 1：Course Introduction
Section 1 - Course Information
14:15
Lecture 2：Vector Calculus
Section 1 - Vector Functions (1)
40:12
Section 2 - Vector Functions (2)
19:32
Section 3 - Curve in 3D Space
25:30
Section 4 - Example of 3D curve
46:31
Section 5 - Differential Operators: Intro
03:30
Section 6 - Differential Operators: Gradient
43:13
Section 7 - Differential Operators: Divergence
31:59
Section 8 - Differential Operators: Curl
21:48
Section 9 - Differential Operators: Curl (2)
21:52
Section 10 - Line Integrals
30:04
Section 11 - Line Integrals: Path Independence
44:16
Section 12 - Green's Theorem
52:56
Section 13 - Surface Integrals
52:28
Section 14 - Flux Integrals
34:04
Section 15 - Gauss' Divergence Theorem
31:48
Section 16 - Stokes Theorem
10:00
Section 17 - Stokes Theorem (2)
45:05
Lecture 3：Fourier Analysis
Section 1 - Introduction
10:16
Section 2 - Function space, orthogonal basis
53:43
Section 3 - Function space, orthogonal basis (2)
33:41
Section 4 - Convergence of Fourier Series
11:36
Section 5 - Example
31:18
Section 6 - Even and Odd Function
17:59
Section 7 - Half-range Expansions
24:37
Section 8 - Complex Fourier Series
24:39
Section 9 - Fourier Integrals
24:48
Section 10 - Fourier Integrals (2)
57:19
Section 11 - Fourier Transform: Definition
27:06
Section 12 - Fourier Transform: Variation
14:10
Section 13 - Fourier Transform: Properties
09:22
Section 14 - Fourier Transform: Properties (2)
51:21
Section 15 - Fourier Transform Pairs
15:16
Section 16 - Transform of Some Elementary Functions
43:43
Section 17 - Discrete Fourier Transform (DFT)
49:04
Lecture 4：Sturm-Liouville Problem (Theory)
Section 1 - Introduction, Cases Discussion
53:53
Section 2 - The Solution of S.-L. Problems
52:20
Section 3 - Examples
49:46
Lecture 5：Partial Differential Equations
Section 1 - Basic Concepts of PDEs
23:30
Section 2 - Wave Equations
24:48
Section 3 - 1D Wave Equations
53:47
Section 4 - 1D Wave Equations (2)
48:06
Section 5 - Demonstration of Examples
31:08
Lecture 6：Heat Equation
Section 1 - Introduction
23:58
Section 2 - 1D Heat Equation and Application to Non-homogeneous Problem
44:52
Section 3 - 1D Heat Equation for an Infinite x-Domain
49:51
Section 4 - 2D Heat Equation and Steady-State Solution
50:31
Section 5 - Laplace Equation in 2D
52:40
Section 6 - Laplace Equation in 2D (2)
28:35
Section 7 - 2D Equations
51:51
Section 8 - 2D Wave Equations in Polar Coordinates
55:23
Section 9 - Laplacian in Spherical Coordinates
47:18
Lecture 7：Complex Analysis
Section 1 - Basic Concepts of Complex Number and Complex Plane
30:58
Section 2 - Complex Function
23:44
Section 3 - Cauchy-Riemann Equations and Potential Theory in Complex Functions
54:41
Section 4 - Introduction to Analytic Functions and Complex Integration
22:20
Section 5 - Complex Integration and Introduction to Cauchy's Integral Theorem
52:00
Section 6 - Cauchy's Integral Theorem
41:56
Section 7 - Terminology in Cauchy's Integral Theorem: Zeros, Poles, and Singularities
18:29
Section 8 - Residue Theorem and Case Analysis of Complex Poles
30:55
Section 9 - Applying the Residue Theorem to Evaluate Real-valued Integrals
57:23
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Prof. Ching Chang
Prof. Ching Chang

Dept. Power Mechanical Engineering

Research Field

The Modeling and Computations for Fluid Dynamics, with Applications in Renewable Energy, Aerodynamics, and Biologically Inspired Engineering.

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