一、課程說明(Course Desc<x>ription) 
<br>
<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 
<br>
<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>Dennis Zill, "Advanced Engineering Mathematics", Jones & Bartlett, 6th Ed
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<br>三、參考書籍(References) 
<br>
<br>Michael D. Greenberg, "Advanced Engineering Mathematics" 2nd ed.,  
<br>(1998 by Prentice-Hall International, 2006 by Pearson Education) 
<br>
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<br>四、教學方式(Teaching Method) 
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<br>3.5 hours lecture per week。 
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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: Qualitative solution and numerical methods (Chapter 6)
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<br>Week 4-6: Linear ODE (homogeneous, non-homogeneous): Euler's integrating 
<br>factor method, Lagrange's variations of parameter method, Separable 
<br>equation, exact equation and integrating factors. (Chapter 2)
<br>
<br>Week 7-8: 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 
<br>constant coefficients (characteristic equation, distinct roots, repeated 
<br>roots ), harmonic oscillator (free oscillation) (Chapter 3)
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<br>Week 9-10: Linear nonhomogeneous equation with constant coefficients (method 
<br>of undetermined coefficients, method of inverse operators), Forced harmonic 
<br>oscillator, system of linear ODE with constant coefficients, Linear ODE with 
<br>variable coefficients (Cauch-Euler equation, Method of reduction of order, 
<br>Method of variation of parameters)(Chapter 3)   
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<br>Week 11-13: Laplace transform, inverse Laplace transform, special functions, 
<br>application to the solution of ODE. (Chapter 4)
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<br>Week 14-15: power series method, Method of Frobenius, Legendre equation, 
<br>Gamma function, Bessel equation, modified Bessel equation (Chapter 5)
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<br>六、成績考核(Evaluation) 
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<br>Midterm exam I(30~33%)
<br>Midterm exam I(30~34%)
<br>Final exam    (30~33%)
<br>小考&點名      (0~10%)
<br>
<br>*課堂上仍會給回家作業讓同學練習但不計分
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<br>七、可連結之網頁位址 (Web site)
<br>https://lms.nthu.edu.tw