課程說明：本學期為劉教授第一次開這門課。因此課本尚未決定，可能會採講義與板書為主，著重在作業的實
<br>作。根據劉教授20餘年的經驗，數值求解是將工數的知識落實在研究的基本素養。某種角度看來，可以將電腦求
<br>解或是模擬，當作是數學的實驗。
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<br>以下暫定內容參考先前開課教授的規劃。
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<br>參考書籍：
<br>E. Kreyszig, Advanced Engineering Mathematics, 10th Ed. (John Wiley and Sons Inc., 
<br>2011). Topics to cover: Ch. 4, 5, 12, 19, 20, 21
<br>
<br>W. Cheney and D. d Kincaid, Numerical Mathematics and Computing, 6th Ed. 
<br>(Brooks/Cole, 2008). Topics to cover: Ch. 1-5, 6, 7, 8, 10-11,12, 14, 15
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<br>教學方式：板書、講義、電腦程式討論
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<br>教學進度：
<br>1. Basics of Numerical Methods: 4 weeks
<br>– Numerical Differentiations
<br>– Numerical Integrations
<br>– Numerical Linear Algebra
<br>– Runge-Kutta methods for ODEs
<br>
<br>2. Numerical Methods for PDEs: 5 weeks
<br>– PDEs and Finite-Difference method
<br>– Parabolic problems
<br>– Hyperbolic problems
<br>– Elliptic Problems
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<br>Eigenfunction Expansion: (Special functions) 2 weeks
<br>– Bessels functions in Cylindrical coordinates
<br>– Spherical coordinates
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<br>4. Impulse-response Methods: (Green’s function) 2 weeks
<br>– Greens function for ODEs
<br>– Greens function for Dirac Delta function 
<br>– Greens function for Poissons equation
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<br>5. Calculus of Variations Methods: 2 week
<br>– Variational problem
<br>– Ritz Finite Element method
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<br>成績考核（暫定）
<br>- 作業+課堂參與 50%
<br>- 期中考 20%
<br>- 期末考 30%
<br>