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
99-1
140350
應用數學
1
3.0
3
★
楊安石
職能源所
33
0
教學大綱與進度:
教師姓名
楊安石
Email
asyang@ntut.edu.tw
最後更新時間
2010-08-11 15:22:01
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,進而訓練學生具備分析工程系統之數學建模能力。 其課程大綱為: 單元主題1:First-Order Differential Equations;Linear Differential Equations of Second and Higher Order 單元主題2:Series Solutions: Power Series Method 單元主題3:Laplace Transforms 單元主題4:Matrices, Eigenvalues, Eigenvectors 單元主題5:Vector Differential Calculus 單元主題6:Vector Integral Calculus 單元主題7:Fourier Series 單元主題8:Partial Differential Equations
課程進度
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 4) Higher Order Homogenous Linear Eq. with Constant Coefficients; Nonhomogeous Linear ODEs 5) Power Series Method; Theory of the Power Series Method 6) Legendre’s Equation; Legendre Polynomials Pn(x) 7) Laplace Transform; Transformations of Derivatives and Integrals Diff. Eq 8) Unit Step Function; Differentiation and Integration of Laplace Transforms; Convolution. Integral Eq. 9) 期中考 10) Matrices, Vectors, Matrix Multiplication;Linear Systems of Eqs.; Gauss Elimination;Rank of a Matrix; Linear Independence; Vector Space 11) Solutions of Linear System; Determinants; Cramer’s Rule; Inverse of a Matrix 12) Eigenvalues, Eigenvectors; Some Applications of Eigenvalue Problems; Symmetric, Skew-Symmetric, and Orthogonal Matrices 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
1) 平時成績20%(含上課表現、出席率) 2) 期中成績40% 3) 期末成績40%
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:
Advanced Engineering Mathematics (9th Edition, John Wiley) Authors: Erwin Kreyszig
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