一、課程說明
<br>This is a mandatory mathematics course for students of the second year of study in the ESS 
<br>department. 
<br>The topics of this course include: 
<br>(1) Ordinary differential equations: 1st order ODEs, 2nd order ODEs, higher order ODEs, and 
<br>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) 
<br>Zill & Wright, "Advanced Engineering Mathematics", 6th Ed., Jones & Bartlett (2017) 
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<br>三、參考書籍(References) 
<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) 
<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>Office Hours,
<br>Tuesday, 1:00 - 2:00 pm 
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<br>五、教學進度(Syllabus) 
<br>Part 1. Introduction to Differential Equations
<br>Week 1: Definitions and Terminology and Initial-Value Problems
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<br>Part 2. First-Order Differential Equations
<br>Week 2, 3: Separable Equations, Linear Equations, Exact Equations, Solutions by Substitution 
<br>(Bernoulli equation, Riccati equation), and an Introduction to Numerical Method 
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<br>Part 3. Higher-Order Differential Equations
<br>Week 4, 5: Theory of Linear Equations, Reduction of Order, and Homogeneous Linear Equations 
<br>with constant coefficients. 
<br>Week 6, 7: Undetermined Coefficients, Variation of Parameters, Cauchy-Euler Equations, and 
<br>Nonlinear equation.
<br>Week 8, 9: Linear Models of Initial-Value and Boundary-Value problems, Green’s Functions, and 
<br>Solving System of Linear Equations.   
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<br>Part 4. Series Solutions of Linear Differential Equations
<br>Week 10, 11: Power Series Solutions and the Method of Frobenius 
<br>Week 12: Bessel Functions and Legendre Functions
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<br>Part 5. The Laplace Transform
<br>Week 13, 14: Definition of Laplace transform, The Inverse Transform and Transform of Linear 
<br>Equations, Translation Theorems, Derivative of Transforms, Transform Integral
<br>Week 15: Transform of a periodic Function, and System of Linear Differential Equations.
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<br>六、成績考核(Evaluation) 
<br>Attendance Quiz (10%)
<br>Homeworks (15%)
<br>First Midterm Exam (25%) 
<br>Second Midterm Exam (25%)
<br>Final Exam (25%)