G2011D 教學大綱表

教學大綱表 (113學年度第1學期)

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課程名稱 Course Title	(中文) 工程數學(一) (英文) Engineering Mathematics			開課單位 Departments	機械與材料工程學系
				課程代碼 Course No.	G2011D
授課教師 Instructor	魏哲弘
學分數 Credit	3.0	必/選修 core required/optional	必修	開課年級 Level	大二
先修科目或先備能力(Course Pre-requisites)：Calculus
課程概述與目標(Course Overview and Goals)：1st order differential equation 2nd order differential equation Laplace Transform Series Solution for 2nd order differential equation
教科書(Textbook)	Dennis G. Zill Advanced Engineering Mathematics Jones and Bartlett Publishers
參考教材(Reference)	Erwin Kreyszig Advanced Engineering Mathematics John Wiley & Sons 1999

課程大綱 Syllabus			學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
序 No.	單元主題 Unit topic	內容綱要 Content summary	學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
1	Introdoction to Differential Equation	Review of Calculus especially integration techniques like substitution, integration by parts and integration by substitution	Bridge the link between calculus and 1st order differential equations
2	1st Order Differential Equation	Introduction to Differential Equation like linearity vs. nonlinearity, order and power and 1st order differential equation solving techniques	understand what is differential equations, the application of differential equations
3	1st Order Differential Equation	Introduction the techniques like separation and integration factors to solve 1st Order Differential Equations	Learn the solving techniques separation and integration factors (linear equation) to solve 1st order differential equations
4	1st Order Differential Equation	1st order ODE solving techniques excat and exact with integration factors	learn the techniques of solving excat and exact with integration factors in 1st oder ODE
5	1st Order Differential Equation	1st order ODE solving techniques like substitution, Bernoulli and homogeneous type equations	Learn the techniques of substitution to solve Bernoulli, homogeneous types of ODEs
6	2nd order Differential Equations	The defintion of 2nd order Differential Equations, homoegenous and non-homogeneous type equations. Constant coefficient 2nd order Differential Equations Euler 2nd order Differential Equations Reduction of order	Learn 2nd order Differential Equations, and what are homoegenous and non-homogeneous type equations two types of homoegenous type equations: 1.Constant coefficient 2. Euler
7	2nd order Differential Equations	Non-homogeneous type of 2nd order ODE undetermined coefficient method	Learn how to solve Non-homogeneous type of 2nd order ODE by undetermined coefficient method
8	2nd order Differential Equations	Solve non-homogeneous 2nd order ODE by variation of parameters methods	Learn how to solve variable coefficient non-homogeneous 2nd order ODE by variation of parameters methods
9	Midterm	Midterm	Midterm
10	Laplace Transform	1. What is Laplace Transform 2. Basic function of Laplace Transform 3. The convergence condition of Laplace Transform	understanding 1. What is Laplace Transform 2. Basic function of Laplace Transform
11	Laplace Transform	Basic functions Inverse Laplace Transform 1st shift theorem 2nd shift theorem	How to take inverse inverse transform of basic functions What is 1st shift theorem? The applications? What is 2nd shift theorem? The applications?
12	Laplace Transform	Laplace transform more advanced topics	learn how to calculate: the Laplace Transform involiving functions times t the Laplace Transform involiving functions divided by t the inverse Laplace Transform involiving functions times s the inverse Laplace Transform involiving functions divided by s
13	Laplace Transform	Unit step functions Impulse functions periodic functions	learn to calculate unit step functions, Impulse functions and periodic functions
14	Laplace Transform	convolution applation of convolution	the operation of convolution why we need convolution application of convolution
15	Series Solution of 2nd order ODE	series solution of linear equations power series solution solution about ordinary points	why we need series solution what is power series
16	Series Solution of 2nd order ODE	solution about singular points	what are singular points how to obtain series solution about singular points
17	Series Solution of 2nd order ODE	special functions	Bessel functions Legendre functions application of Bessel functions application of Legendre functions
18	Final Exam	Final Exam	Final Exam

彈性教學週活動規劃

序 No.	實施期間 Period	實施方式 Content	教學說明 Teaching instructions	彈性教學評量方式 Evaluation	備註 Notes
1	起:2024-01-01 迄:2024-01-12	5.小專題 Project	不同專題讓同學分組進行專題研究	根據專題報告評分

教學要點概述：
1.自編教材 Handout by Instructor：
■ 1-1.簡報 Slids
□ 1-2.影音教材 Videos
■ 1-3.教具 Teaching Aids
■ 1-4.教科書 Textbook
□ 1-5.其他 Other
□ 2.自編評量工具/量表 Educational Assessment
□ 3.教科書作者提供 Textbook

成績考核 Performance Evaluation：期末考：25% 期中考：25% 彈性教學：10% 平時考：40%

教學資源(Teaching Resources)：
□ 教材電子檔(Soft Copy of the Handout or the Textbook)
□ 課程網站(Website)
扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php