G2011E 教學大綱表

教學大綱表 (112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.	G2011E
授課教師 Instructor	吳臺一
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)：Solve 1st order differential equation Solve 2nd order differential equation Understand what is linear algebra Understand the transpose, rank, inverse, and determinant of a matrix Understand the linear space
教科書(Textbook)	Erwin Kreyszig Advanced Engineering Mathematics John Wiley & Sons 1999
參考教材(Reference)	Dennis G. Zill Advanced Engineering Mathematics Jones and Bartlett Publishers

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	Introduction to Matrix	Basic Matrix definition and operation, the addition and subtraction of matrix, the mutlipication of matrix	The basic definition and operation of a matrix, and how to add and substract two matrix, and the multiplication of matrix
11	Row echelon form	Use Gauss elimination to solve systems of equations, row echelon form	The elementary row operation (Gauss eliminaion), row echelon form
12	Rank and System of Equations	the conecnpt of rank, system of equation, determinant	use elementary row operation to calculate rank and the solution of homogeneous and non-homogeneous solutions, the calculation of determinant
13	Determinant	The calculation of determinant	how to use cofactor expansion and elementary row operation to calculate determinant
14	Matrix Inverse	The calculation of determinant and inverse of a matrix	how to use cofactor expansion and elementary row operation to calculate determinant, and use adjoint matrix and elementary row operation to calculate matrix inverse
15	Eigenvalues and Eigenvectors	The definition of eigenvalues and eigenvectors, double roots and triple roots of eigenvalues in a 3x3 matrix	The calculate the eigenvalues and eigenvectors of a matrix, and the special cases of double roots and triple roots of eigenvalues in a 3x3 matrix
16	Digonization	Diagonization, The powers of matrices, Cayley-Hamilton Theorem	Use eigenvectors to form a matrix to diagonize a matrix, understand Cayley-Hamilton Theorem to calculate the powers of matrices
17	Orthogonal Matrix and Quadratic Forms	The definition of Orthogonal Matrix and the application to Quadratic Forms	The definition of orthogonal matrix and why it is important to convert to a quadratic forms
18	Final Exam	Final Exam	Final Exam

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：

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：http://eboard.ttu.edu.tw/ttuwebpost/showcontent-news.php?id=504