一、課程說明(Course Description) 
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<br>This course is the first one in a series of  4 engineering mathematics courses in the ESS department.  This course will focus on the methods or techniques in solving ordinary differential equations (ODEs), as well as some of their applications in engineering problems.  If time allows, a brief introduction to
<br>basics of partial differential equations will also be given.  A
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<br>The topics covered in this course include:
<br>1. First order ODEs
<br>2. Second order ODEs
<br>3. Higher order ODEs
<br>4. Systems of ODEs
<br>5. Special functions and power series method 
<br>6. Laplace Transform 
<br>7. Basics of partial differential equations
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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>Lecture time: Tuesday & Friday 8:20-9:50. (no breaks) 
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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,  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>Midterms I & II    (40%)
<br>Final exam         (20%)
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<br>七、可連結之網頁位址 (Web site)
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<br>NTHU e-learning system - iLMS：http://lms.nthu.edu.tw