一、課程說明(Course Desc<x>ription) 
<br>
<br>This is a mandatory mathematics course for students in the second year of ESS department. The 
<br>topics of this course include:
<br>
<br>1) Ordinary Differential Equations: 1st order ODEs, 2nd order ODEs, higher order ODEs, systems of 
<br>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>
<br>
<br>二、指定用書(Text Books) 
<br>
<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>
<br>
<br>四、教學方式(Teaching Method) 
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<br>4 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 terminology
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<br>Week 2,3: Linear ODE (homogeneous, non-homogeneous): Euler's integrating factor method, 
<br>Lagrange's variations of parameter method, Bernoulli equation, Riccati equation, d'Alembert-
<br>Lagrange equation, Separable equation, exact equation and integrating factors.
<br>
<br>Week 4,5,6: Linear ODE of 2nd order or higher, linear independent/dependent, Wronskian, basis set 
<br>of solution of DE, existence and uniqueness for Initial-Value Problem,  homogeneous equation with 
<br>constant coefficients (characteristic equation, distinct roots, repeated roots ), harmonic oscillator 
<br>(free oscillation)
<br>
<br>Week 7,8,9: Linear nonhomogeneous equation with constant coefficients (method of undetermined 
<br>coefficients, method of inverse operators), Forced harmonic oscillator, system of linear ODE with 
<br>constant coefficients, Linear ODE with variable coefficients (Cauch-Euler equation, Method of 
<br>reduction of order, Method of variation of parameters)   
<br>
<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, 
<br>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 
<br>solution of ODE.
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<br>六、成績考核(Evaluation) 
<br>
<br>Homeworks    (30%)
<br>Quiz         (0%)
<br>Midterm exam (35%)
<br>Final exam   (35%)
<br>點名         (0%)
<br>
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<br>七、可連結之網頁位址 (Web site)
<br>https://lms.nthu.edu.tw