一、課程說明(Course Description) 
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<br>This is a mandatory mathematics course for students in the second year of ESS department. The topics of this course include:
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<br>1) Ordinary Differential Equations: 1st order ODEs, 2nd order ODEs, higher 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
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<br>二、指定用書(Text Books) 
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<br>Erwin Kreyszig, "Advanced Engineering Mathematics", Wiley (2011), 10th Ed
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<br>三、參考書籍(References) 
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<br>Michael D. Greenberg, "Advanced Engineering Mathematics" 2nd ed.,  
<br>(1998 by Prentice-Hall International, 2006 by Pearson Education) 
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<br>四、教學方式(Teaching Method) 
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<br>3 hours lecture per week。 
<br>上課時間: 每週二及週五上午 8:30-9:50 (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 terminology
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<br>Week 2,3: Linear ODE (homogeneous, non-homogeneous): Euler's integrating factor method, Lagrange's variations of parameter method, Bernoulli equation, Riccati equation, d'Alembert-Lagrange equation, Separable 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, Wronskian, basis set of solution of DE, existence and uniqueness for Initial-Value Problem,  homogeneous equation with constant coefficients (characteristic equation, distinct roots, repeated roots ), harmonic oscillator (free oscillation)
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<br>Week 7,8,9: Linear nonhomogeneous equation with constant coefficients (method of undetermined coefficients, method of inverse operators), Forced harmonic oscillator, system of linear ODE with constant coefficients, Linear ODE with variable coefficients (Cauch-Euler equation, Method of reduction of order, Method of variation of parameters)   
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<br>Week 10,11:  power series method, Method of Frobenius
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<br>Week 12,13: Legendre equation, Gamma function, Bessel equation, modified Bessel equation, exponential integral, equations reducible to Bessel equations
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<br>Week 14,15: Laplace transform, inverse Laplace transform, special functions, application to the solution of ODE.
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<br>六、成績考核(Evaluation) 
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<br>Homeworks    (20%)
<br>Quiz         (20%)
<br>Midterm exam (30%)
<br>Final exam   (30%)
<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