一、課程說明(Course Desc<x>ription) 
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<br>This is a mandatory mathematics course for students in the second year of 
<br>ESS department. The topics of this course include:
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<br>1) Ordinary Differential Equations: 1st order ODEs, 2nd order ODEs, higher 
<br>order ODEs, systems of ODEs
<br>2) Special functions and power series method 
<br>3) Laplace Transform 
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<br>* 課程預備知識: 需已修習過微積分
<br>
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<br>二、指定用書(Text Books) 
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<br>Zill/Wright/Ding, Engineering Mathematics, Metric Edition, Cengage, Taipei, 
<br>Taiwan (2019)
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<br>三、參考書籍(References) 
<br>
<br>1. Erwin Kreyszig, "Advanced Engineering Mathematics", 10th Ed, Wiley (2011)
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<br>2. Michael D. Greenberg, "Advanced Engineering Mathematics" 2nd ed.,  (1998 by 
<br>Prentice-Hall International, 2006 by Pearson Education) 
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<br>四、教學方式(Teaching Method) 
<br>板書上課，150 mins lecture per week。
<br>上課時間: 每週一 10:10~11:30, 每週三 8:40~9:50 (課程中間不下課休息)
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<br>五、教學進度(Syllabus) 
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<br>Week 1: Introduction to Differential Equation, definition of basic 
<br>terminology
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<br>Week 2,3: Linear ODE (homogeneous, non-homogeneous): Euler's integrating 
<br>factor method, Lagrange's variations of parameter method, Bernoulli 
<br>equation, Riccati equation, d'Alembert-Lagrange equation, Separable 
<br>equation, exact equation and integrating factors.
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<br>Week 4,5,6: Linear ODE of 2nd order or higher, linear independent/dependent, 
<br>Wronskian, basis set of solution of DE, existence and uniqueness for 
<br>Initial-Value Problem,  homogeneous equation with constant coefficients 
<br>(characteristic equation, distinct roots, repeated roots ), harmonic 
<br>oscillator (free oscillation)
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<br>around Week 7:  第一次期中考
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<br>Week 8,9,10: Linear nonhomogeneous equation with constant coefficients 
<br>(method of undetermined coefficients, method of inverse operators), Forced 
<br>harmonic oscillator, system of linear ODE with constant coefficients, Linear 
<br>ODE with variable coefficients (Cauch-Euler equation, Method of reduction of 
<br>order, Method of variation of parameters)   
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<br>Week 11,12:  power series method, Method of Frobenius
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<br>around Week 13: 第二次期中考
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<br>Week 14,15: Legendre equation, Gamma function, Bessel equation, modified 
<br>Bessel equation, exponential integral, equations reducible to Bessel 
<br>equations
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<br>Week 16,17: Laplace transform, inverse Laplace transform, special functions, 
<br>application to the solution of ODE.
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<br>Week 18: Final exam
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<br>六、成績考核(Evaluation) 
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<br>Homework    (25%)
<br>1st Midterm exam (25%)
<br>2nd Midterm exam (25%)
<br>Final exam   (25%)
<br>點名         (學期成績加分用)
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<br>七、可連結之網頁位址 (Web site)
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<br>N/A