11210 工程數學一

# Required Courses # Undergraduate Program
7個章節 / 54個單元 / 29小時25分鐘39秒
第 1 章：Course Introduction
單元 1
05:26
第 2 章：First-Order Ordinary Differential Equations (ODEs)
單元 1
27:59
單元 2
33:28
單元 3
49:49
單元 4
39:48
單元 5
43:30
單元 6
10:15
單元 7
29:15
單元 8
10:01
第 3 章：Second-Order Linear ODEs
單元 1
30:07
單元 2
41:48
單元 3
48:04
單元 4
33:16
單元 5
11:03
單元 6
35:55
單元 7
17:27
單元 8
43:54
單元 9
39:07
單元 10
10:08
單元 11
07:31
第 4 章：Higher Order ODEs
單元 1
37:50
單元 2
19:29
單元 3
24:47
第 5 章：Systems of ODE
單元 1
01:27:34
單元 2
41:09
單元 3
46:56
單元 4
13:34
單元 5
40:57
單元 6
58:52
單元 7
38:25
單元 8
47:24
單元 9
36:18
第 6 章：Laplace Transform
單元 1
16:41
單元 2
38:12
單元 3
17:13
單元 4
29:20
單元 5
44:31
單元 6
21:19
單元 7
29:49
單元 8
19:13
單元 9
16:58
單元 10
11:54
單元 11
27:07
第 7 章：Series Solution of ODEs
單元 1
28:12
單元 2
53:51
單元 3
14:17
單元 4
32:26
單元 5
43:09
單元 6
45:22
單元 7
47:18
單元 8
40:38
單元 9
46:18
單元 10
48:25
單元 11
32:20
課程介紹
課程總時長｜ 29小時25分鐘39秒
單元數｜ 7個章節 54個單元

Brief course descriptions

Engineering Mathematics is a required course for the Department of Chemical Engineering, taught over two semesters. It covers the mathematical foundations necessary for specialized chemical engineering subjects, such as Transport Phenomena, Reaction Engineering, and Process Control. Topics include Ordinary Differential Equations (ODE), Linear Algebra, Vector Calculus, Fourier Analysis, and Partial Differential Equations (PDE), with examples drawn from chemical engineering applications whenever possible. The content of Engineering Mathematics (I) includes first-order, second-order, and higher-order ODEs and their solutions; systems of first-order ODEs; Laplace Transforms and their applications; Power Series Solutions; and Sturm-Liouville problems.

Course keywords

工程數學(Engineering Mathematics), 常微分方程式(Ordinary Differential Equation), 拉普拉斯轉換(Laplace Transform), 冪級數解(Power Series Solution), 斯圖姆-劉維爾問題(Sturm-Liouville Problem)

Textbook

Advanced Engineering Mathematics, E. Kreyszig, 10th edition Update (2018).

Course Topics

Topic 1 (Ch1) – First-Order Ordinary Differential Equations (ODEs)
Topic 2 (Ch2) – Second-Order Linear ODEs
Topic 3 (Ch3) – Higher-Order Linear ODEs
Topic 4 (Ch4) – Systems of ODEs, Phase Plane, Qualitative Methods
Topic 5 (Ch6) – Laplace Transforms
Topic 6 (Ch5) – Series Solutions of ODEs, Special Functions

課程章節
第 1 章：Course Introduction
單元 1 - Overall View
05:26
第 2 章：First-Order Ordinary Differential Equations (ODEs)
單元 1 - Separable Ordinary Differential Equation
27:59
單元 2 - Separable Ordinary Differential Equation (continued)
33:28
單元 3 - Exact Differential Equation, Integrating Factor
49:49
單元 4 - Integrating Factors
39:48
單元 5 - Linear ODEs, Hormone Level
43:30
單元 6 - Bernoulli Equation
10:15
單元 7 - Existence Theorem
29:15
單元 8 - Uniqueness Theorem
10:01
第 3 章：Second-Order Linear ODEs
單元 1 - Homogeneous Linear ODEs of Second Order, Foundamental Theorem, Initial/Boundary Value Problem18
30:07
單元 2 - Initial Value Problem and Basis General Solution
41:48
單元 3 - Solve Homogeneous Linear ODEs with Constant Coeff. by Algebra
48:04
單元 4 - Solve Homogeneous Linear ODEs with Constant Coeff. by Algebra (continued), Introduction of Euler Formula
33:16
單元 5 - Form of Euler-Cauchy Equations
11:03
單元 6 - Roots of Euler-Cauchy Equations
35:55
單元 7 - Existence & Uniqueness of Solutions
17:27
單元 8 - Form of Nonhomogeneous ODEs of 2nd Order, Methods of Undetermined Coefficients (Basic rule)
43:54
單元 9 - Methods of Undetermined Coefficients (Modification Rule and Sum rule)
39:07
單元 10 - Solution by Variation of Parameters (by Lagrange's), Definition of Wronskian
10:08
單元 11 - An Example of Variation of Parameters
07:31
第 4 章：Higher Order ODEs
單元 1 - Homogeneous Linear ODEs
37:50
單元 2 - Homogeneous Linear ODEs (continued)
19:29
單元 3 - Nonhomogeneous Linear ODEs
24:47
第 5 章：Systems of ODE
單元 1 - Theory of Systems of Linear 1st order Differential Equations
01:27:34
單元 2 - Introduction of Eigenvalues and Eigenvectors
41:09
單元 3 - Solutions of X'=AX when A is constant
46:56
單元 4 - Method of Finding Eigenvalues and Eigenvectors
13:34
單元 5 - Solutions of X'=AX when A has complex eigenvalues
40:57
單元 6 - Solutions of X'=AX when A does not have n linearly independent Eigenvectors
58:52
單元 7 - Solutions of X'=AX+G
38:25
單元 8 - Solution of X'=AX by Diagonalizing A
47:24
單元 9 - Solution of X'=AX+G by Diagonalizing A
36:18
第 6 章：Laplace Transform
單元 1 - Introduction
16:41
單元 2 - Laplace Transform (Linearity, 1st Shifting Theorem)
38:12
單元 3 - Laplace Transform (Linearity, 1st Shifting Theorem) (continued)
17:13
單元 4 - Laplace Transform of Derivatives and Integrals
29:20
單元 5 - Solve the Differential Equations, IVP
44:31
單元 6 - Solve the Differential Equations, IVP (continued)
21:19
單元 7 - Unit Step Function (Heaviside Function), Second Shifting Theorem
29:49
單元 8 - Second Shifting Theorem (continued)
19:13
單元 9 - Short Impulses, Dirac's Delta Function
16:58
單元 10 - Convolution
11:54
單元 11 - Convolution (continued)
27:07
第 7 章：Series Solution of ODEs
單元 1 - Power Series Method
28:12
單元 2 - Power Series Method (continued)
53:51
單元 3 - Power Series Method (continued)
14:17
單元 4 - Legendre's Equation, Legendre Polynomials
32:26
單元 5 - Legendre's Equation, Legendre Polynomials (continued)
43:09
單元 6 - Extended Power Series Method: Frobenius Method
45:22
單元 7 - Extended Power Series Method: Frobenius Method (continued)
47:18
單元 8 - Extended Power Series Method: Frobenius Method (continued)
40:38
單元 9 - Bessel's Equation, Bessel's Functions
46:18
單元 10 - Bessel's Equation, Bessel's Functions (continued)
48:25
單元 11 - Bessel's Equation (General Solution & Linear Independence)
32:20
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潘詠庭 教授
潘詠庭 教授

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