工程數學(一)

臺北科技大學 115-1 學期課程，課號 362362。

課程大綱

1. 一階常微分方程 2. 二階常微分方程 3. 線性聯立微分方程 4. Laplace Transform

課程進度

週次/ Week Topics教學進度 1 Introduction 2 1.0 First-Order Differential Equations 1.1 Basic Concepts and Ideas 3 1.2 Separable Differential Equations 4 1.3 Exact Differential Equations. Integrating Factors 5 1.4 Linear Differential Equations. Bernoulli Equation 6 2.0 Linear Differential Equations of Second and Higher Order 2.1 Homogeneous Linear Equations of Second Order 2.2 Second Order Homogeneous Equations with Constant Coefficients 7 2.3 Case of Complex Roots. Complex Exponential Function 2.4 Euler-Cauchy Equation 8 2.6 Nonhomogeneous Equations 2.7 Solution by Undetermined Coefficients. Solution by Variation of Parameters 9 Midterm Exam 10 3. System of Differential Equations, Phase Plane, Qualitative Methods 3.1 Vectors, Matrices, Eigenvalues 11 3.2 Homogeneous Systems with Constant Coefficients. 12 3.2 Homogeneous Systems with Constant Coefficients. 13 3.3 Qualitative Methods for Nonlinear Systems 3.4 Nonhomogeneous Linear System 14 4. Laplace Transforms 4.1 Laplace Transform. Inverse Transform. Linearity. Shifting 15 4.2 Transforms of Derivatives and Integrals. Differential Equations 4.3 Unit Step Function. Second Shifting Theorem, Dirac’s Delta Function 16 Final Exam 17 參與課程相關作業、作品調查 18 參與課程相關作業、作品調查

評量方式

Attendance, Homework, Quizzes, Tests, Flexible Learning, Midterm, Final Exam: 共100% (缺席者以零分計算)

教材

【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 參考書目： 1. Zill, D.G. & Wright, W.S. (2014). Advanced Engineering Mathematics. 5th Ed. The Jones and Bartlett Publishers, USA. 2. Erwin Kreyszig (2011). Advanced Engineering Mathematics. 10th Ed. John Wiley & Sons, Inc. 3. Peter O’Neil (2013). Advanced Engineering Mathematics. Brooks/Cole Publishing Company.