課程名稱 (中文) 工程數學(一) (英文) Engineering Mathematics 開課單位 機械工程學系 課程代碼 G2011E 授課教師 戴兢志 學分數 3.0 必/選修 必修 開課年級 大二 先修科目或先備能力：微積分 課程概述與目標：提供同學在學習微積分後繼續在數學上有進一步了解，並學習以數學為工具，與工程問題相結合。第一學期主要為常微分方程式與線性代數兩部分。課程內容包括：一階及二階之常微分方程式及其解法；矩陣及其應用。 教科書 自編教材 參考教材 (1)Zill and Wright, Advanced Engineering Mathematics, 6th ed., Jones and Bartlett Publishers. (2) Peter V. O’Neil, Advanced Engineering Mathematics, 6th ed., Thomson. (2007) (3)Mathematical Handbook and Table.
 課程大綱 學生學習目標 單元學習活動 學習成效評量 備註 週 單元主題 內容綱要 1 Introduction 1. 智慧財產及專業倫理宣導 2. Introduction 3. Review the basis of Calculus 1. 智慧財產及專業倫理宣導 2. Introduction 3. Review the basis of Calculus 講授 2 First-order differential equations Preliminary concepts - Definitions and Terminoloy Definition of 1. Differential equation 2. Order 3. Linear 4. Solutions 講授 3 First-order differential equations Initial Value Problems 1. Initial Value Problems 2. Initial conditions 3. General solution 4. Particular solution 講授 4 First-order differential equations Separable equations Linear equations Separable equations Linear equations 講授 5 First-order differential equations Exact equations Exact equations 講授 6 Second-order differential equations 1. Preliminary concepts 2. The Linear Homogeneous equations 3. The Nonhomogeneous equations 4. The Constant coefficient Linear Homogeneous equations 1. Preliminary concepts 2. The Linear Homogeneous equations 3. The Nonhomogeneous equations 4. The Constant coefficient Linear Homogeneous equations 講授 平時考 7 Second-order differential equations Undetermined Coefficients Undetermined Coefficients 講授 8 Second-order differential equations Variation of Parameters Variation of Parameters 講授 平時考 9 期中考 期中考 期中考 期中考 10 Matrices and systems of linear equations Matrix algebra 1. Definition of matrices 2. Matrix Addition 3. Matrix multiplication 4. Special matrices 講授 11 Matrices and systems of linear equations Systems of linear algebraic equations 1. Elementary row operations and elementary matrices 2. The row echelon form of a matrix 講授 12 Matrices and systems of linear equations Systems of linear algebraic equations Solution of homogeneous systems of linear equation 講授 13 Matrices and systems of linear equations Rank of a matrix Rank of a matrix 講授 14 Matrices and systems of linear equations 1. Definition of the Determinant 2. Properties of Determinants 1. Definition of the Determinant 2. Properties of Determinants 講授 平時考 15 Matrices and systems of linear equations Inverse of a matrix Inverse of a matrix 講授 16 Matrices and systems of linear equations Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors 講授 平時考 17 Matrices and systems of linear equations Diagonalization of Matrices Diagonalization of Matrices 講授 18 期末考 期末考 期末考 期末考
 教學要點概述： 教材編選： ■ 自編教材 ■ 教科書作者提供 評量方法： 期末考：20%   期中考：20%   其他評量：10%   平時考：40%   作業：10%   教學資源： ■ 教材電子檔 □ 課程網站課程網站：網路硬碟一：math106 扣考規定：http://eboard.ttu.edu.tw/ttuwebpost/showcontent-news.php?id=504