課程資訊
 課程名稱 工程數學一ENGINEERING MATHEMATICS(I) 開課學期 95-1 授課對象 工程科學及海洋工程學系 授課教師 王昭男 課號 ESOE2021 課程識別碼 505 28110 班次 02 學分 3 全/半年 半年 必/選修 必帶 上課時間 星期一3,4(10:20~12:10)星期四7(14:20~15:10) 上課地點 工科202 備註 各組必修。限學號單號總人數上限：50人 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 一、課程簡介: 1. First-order differential equation Basic concept Geometrical meaning of y’=f(x,y) Separable of differential equation Separable equation Exact differential equation Integrating factors Bernoulli equation Orthogonal trajectory of curves Picard iteration 2. Linear differential equations of second and higher order Homogeneous linear equations of second order Second-order homogeneous equation with constant coefficients Case of complex roots Free oscillation Wronskian Nonhomogeneous equations Solution by undetermined coefficients Solution by variation of parameters Forced oscillation Modeling of electric circuits Higher order linear differential equations Higher order linear differential equations with constant coefficients Higher order nonhomogeneous equations 3. Systems of differential equations, phase plane, qualitative methods Introduction: vectors, matrices, eigenvalues Homogeneous systems with constant coefficient Phase plane, critical point Criteria for critical point, Stability Qualtative method for non-linear systems Nonhomogeneous linear systems 4. Series solution of differential equations Power series method Theory of power series method Legendre’s equation Fribenius method Bessel’s equation Bessel’s function of second Sturm-Liouville problem Orthogonal function expansion 5. Laplace transforms Laplace transform, Linearity, Shift Transform of derivatives and integrals Unit step function, Dirac’s delta function Differential and integral of transform Convolution Partial Fractions Systems of Differential equation 二、先修課程:微積分 三、參考書目: E. Kreyszig, “ Advanced Engineering Mathematics”, John Wiley & Sons, INC. 課程目標 課程要求 預期每週課後學習時數 Office Hours 參考書目 指定閱讀 評量方式(僅供參考)
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