教學大綱表
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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
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
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    2 First-order differential equations Preliminary concepts
    - Definitions and Terminoloy
    Definition of
    1. Differential equation
    2. Order
    3. Linear
    4. Solutions
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    3 First-order differential equations Initial Value Problems 1. Initial Value Problems
    2. Initial conditions
    3. General solution
    4. Particular solution
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    4 First-order differential equations Separable equations
    Linear equations
    Separable equations
    Linear equations
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    5 First-order differential equations Exact equations Exact equations
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    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
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    7 Second-order differential equations Undetermined Coefficients Undetermined Coefficients
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    8 Second-order differential equations Variation of Parameters Variation of Parameters
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    9 期中考 期中考 期中考
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    10 Matrices and systems of linear equations Matrix algebra 1. Definition of matrices
    2. Matrix Addition
    3. Matrix multiplication
    4. Special matrices
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    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
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    12 Matrices and systems of linear equations Systems of linear algebraic equations Solution of homogeneous systems of linear equation
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    13 Matrices and systems of linear equations Rank of a matrix Rank of a matrix
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    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
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    15 Matrices and systems of linear equations Inverse of a matrix Inverse of a matrix
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    16 Matrices and systems of linear equations Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors
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    17 Matrices and systems of linear equations Diagonalization of Matrices Diagonalization of Matrices
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    18 期末考 期末考 期末考
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