查詢教學大綱與進度

教學大綱與進度

課程基本資料：

學年期課號課程名稱階段學分時數修教師班級人撤備註

110-1 289540 應用數學 1 3.0 3 ★ 施陽正職能源所 34 0 ◎

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
110-1	289540	應用數學	1	3.0	3	★	施陽正	職能源所	34	0	◎

教學大綱與進度：

教師姓名施陽正

Email f10958@ntut.edu.tw

最後更新時間 2021-08-30 16:00:52

課程大綱本課程主要目標為將數學方法應用在工程問題，課程內容有常微分方程，線性代數，向量微積分，及偏微分方程式等之簡介，訓練同學數學應用於工程計算及研究。內容包括數值方法，機率理論及數學機率等。 The main target of this course is to intoduce mathematical methods ot engineering applications; the course will cover areas in differential equations and vecto calculus. This course will also train students in applying mathematics to engineering calculations and research, such as unmerical methods and statistical methods.

課程進度週次章節內容 1 ■ Reviews ■ Basic Concepts and Ideas ■ Geometrical Meaning of y’=f(x, y) ■ Separable Differential Eq 2 ■ Modeling: Separable Eq. ■ Homogenous Linear Eq. of 2nd Order with Constant Coefficients ■ Euler-Cauchy Eq. 3 ■ Non-homogenous Equations ■ Solution by Undetermined Coefficients ■ Higher Order Homogenous Linear Eq. with Constant Coefficients 4 ■ Nonhomogeous Linear ODEs ■ Power Series Method ■ Theory of the Power Series Method 5 ■ Legendre’s Equation ■ Legendre Polynomials Pn(x) 6 ■第一次期中考(10/19-10/23) 7 ■ Laplace Transform ■ Transformations of Derivatives and Integrals Diff. Eq ■ Unit Step Function 8 ■ Differentiation and Integration of Laplace Transforms ■ Convolution. Integral Eq. ■ Matrices, Vectors, Matrix Multiplication 9 ■ Linear Systems of Eqs.; Gauss Elimination ■ Rank of a Matrix; Linear Independence; Vector Space ■ Solutions of Linear System 10 ■ Determinants; Cramer’s Rule ■ Inverse of a Matrix 11 ■ Eigenvalues, Eigenvectors ■ Some Applications of Eigenvalue Problems ■ Symmetric, Skew-Symmetric, and Orthogonal Matrices 12 ■ 第二次期中考(11/30-12/4) 13 ■ Curves; Tangents, Arc Length ■ Inner & Vector Product; Gradient of a Scalar Field; Directional Derivative ■ Divergence of a Vector Field; Curl of a Vector Field 14 ■ Line Integrals; Vector and Scalar Functions and Fields; Derivatives ■ Double Integrals ■ Surface Integrals 15 ■ Triple Integrals; Divergence Theorem of Gauss ■ Fourier Series; Functions of Any Period p=2L 16 ■ Even and Odd Functions ■ Fourier Integrals & Fourier Transform 17 ■ Basic Concepts of PDE ■ Separation of Variables ■ Similarity Methods 18 期末考

評量方式與標準成績計算方式: 出席考核(減分)，兩次期中考與期末考; 擇優兩次定為期中成績(50%)、期末成績(50%)

使用教材、參考書目或其他 【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】

使用外文原文書：是
Advanced Engineering Mathematics (10th Edition, John Wiley) Authors: Erwin Kreyszig

課程諮詢管道研究室分機: 3517
研究室位置:綜合科館516-1室
Office Hours: 週一、二14:00~17:00

課程對應SDGs指標

備註 ●上課方式：遠距上課

●評量方式：
疫情「一級」學生須到校進行實體測驗
疫情「二級」及「三級」(含)以上警戒，學生在家進行實體測驗
●補充說明資訊：
遠距上課須先下載Microsoft Teams(費)，並連結至上述的上課網址。
學校已將已選課的學生加入[NTUT-Sync]110-1_289540_應用數學的群組

教師姓名	施陽正
Email	f10958@ntut.edu.tw
最後更新時間	2021-08-30 16:00:52
課程大綱	本課程主要目標為將數學方法應用在工程問題，課程內容有常微分方程，線性代數，向量微積分，及偏微分方程式等之簡介，訓練同學數學應用於工程計算及研究。內容包括數值方法，機率理論及數學機率等。 The main target of this course is to intoduce mathematical methods ot engineering applications; the course will cover areas in differential equations and vecto calculus. This course will also train students in applying mathematics to engineering calculations and research, such as unmerical methods and statistical methods.
課程進度	週次章節內容 1 ■ Reviews ■ Basic Concepts and Ideas ■ Geometrical Meaning of y’=f(x, y) ■ Separable Differential Eq 2 ■ Modeling: Separable Eq. ■ Homogenous Linear Eq. of 2nd Order with Constant Coefficients ■ Euler-Cauchy Eq. 3 ■ Non-homogenous Equations ■ Solution by Undetermined Coefficients ■ Higher Order Homogenous Linear Eq. with Constant Coefficients 4 ■ Nonhomogeous Linear ODEs ■ Power Series Method ■ Theory of the Power Series Method 5 ■ Legendre’s Equation ■ Legendre Polynomials Pn(x) 6 ■第一次期中考(10/19-10/23) 7 ■ Laplace Transform ■ Transformations of Derivatives and Integrals Diff. Eq ■ Unit Step Function 8 ■ Differentiation and Integration of Laplace Transforms ■ Convolution. Integral Eq. ■ Matrices, Vectors, Matrix Multiplication 9 ■ Linear Systems of Eqs.; Gauss Elimination ■ Rank of a Matrix; Linear Independence; Vector Space ■ Solutions of Linear System 10 ■ Determinants; Cramer’s Rule ■ Inverse of a Matrix 11 ■ Eigenvalues, Eigenvectors ■ Some Applications of Eigenvalue Problems ■ Symmetric, Skew-Symmetric, and Orthogonal Matrices 12 ■ 第二次期中考(11/30-12/4) 13 ■ Curves; Tangents, Arc Length ■ Inner & Vector Product; Gradient of a Scalar Field; Directional Derivative ■ Divergence of a Vector Field; Curl of a Vector Field 14 ■ Line Integrals; Vector and Scalar Functions and Fields; Derivatives ■ Double Integrals ■ Surface Integrals 15 ■ Triple Integrals; Divergence Theorem of Gauss ■ Fourier Series; Functions of Any Period p=2L 16 ■ Even and Odd Functions ■ Fourier Integrals & Fourier Transform 17 ■ Basic Concepts of PDE ■ Separation of Variables ■ Similarity Methods 18 期末考
評量方式與標準	成績計算方式: 出席考核(減分)，兩次期中考與期末考; 擇優兩次定為期中成績(50%)、期末成績(50%)
使用教材、參考書目或其他	【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】使用外文原文書：是 Advanced Engineering Mathematics (10th Edition, John Wiley) Authors: Erwin Kreyszig
課程諮詢管道	研究室分機: 3517 研究室位置:綜合科館516-1室 Office Hours: 週一、二14:00~17:00
課程對應SDGs指標
備註	●上課方式：遠距上課 ●評量方式：疫情「一級」學生須到校進行實體測驗疫情「二級」及「三級」(含)以上警戒，學生在家進行實體測驗 ●補充說明資訊：遠距上課須先下載Microsoft Teams(費)，並連結至上述的上課網址。學校已將已選課的學生加入[NTUT-Sync]110-1_289540_應用數學的群組