I. 課程目標和大綱: 
<br>Introduction to the mathematical properties of numerical methods and their applications in computational science and engineering. Study and use of numerical methods for solutions of linear systems of equations, non-linear least-squares data fitting, numerical integration of multi dimensional, non-linear equations and systems of initial value ordinary differential equations. More detail is provided in tentative schedule listed below. 
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<br>II. 預備知識: 無擋修但需要基本的微積分和線性代數知識.
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<br>III. 教科書與參考書: 
<br>教科書:
<br>B. Bradie, A friendly introduction to numerical analysis, 2006, Pearson Prentice Hall.
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<br>參考書:
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<br>David Kincaid and Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition, 
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<br>R. L. Burden and J. D. Faires, Numerical analysis, 8th ed., 2005, Thomson Brooks.
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<br>IV. 成績計算方式: 成績是由以下四個項目
<br>(a)  10%  作業成績
<br>(b)  20%  小考
<br>(c)  40%  兩次期中考, 各佔20%
<br>(d)  30%  期末考. 範圍是整個學期的內容
<br>(e)  10%  小組報告
<br>作業:  作業每周五會放在課程網址上. 隔周五上課1:30pm前時交給我或是助教. 1:30pm之後都算是遲交的作業, 遲交的作業可以批改但是以0分計算. 小考時間為演習課時間, 以上機考程式為主. 除非有醫生證明或是家裡急事, 否則沒有補考的機會. 考試不能使用書本或計算機.
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<br>V. 電腦教室資源: 綜三數學系圖書館內的電腦教室都裝有Matlab可以使用.
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<br>VI. 上課的規定: 
<br>上機演習: 每週T6為上機演習時間, 會不定期利用這個時間小考, 所以這堂課時間一定要空出來, 不能衝堂.
<br>作業遲交: 除非有醫生證明或是家裡有急事, 作業遲交一律0分計算.
<br>出席率: 本課沒有出席率的要求.
<br>作弊: 作業抄襲或是考試作弊的情形被抓到且確定後, 該次作業或考試成績已0分計算. 情節重大者會呈報學校.
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<br>VII. 課程網站: 將使用eeclass系統
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<br>VIII. 預定的課程進度表: 
<br> (1 weeks) Mathematical preliminaries and error analysis: Algorithms, convergence, and errors. 
<br>(2 weeks) Solutions of equations in one variable: Bisection, method of false position, fixed point iteration, and Newton's methods. 
<br>(2.5 weeks) Direct methods for solving linear systems: Gaussian elimination and LU factorization, stability and condition number, and pivoting strategies.
<br>(2.5 weeks) Interpolation and polynomial approximation: Lagrange, Hermite, and cubic spline interpolation. 
<br>(3 weeks) Numerical differentiation and integration: Forward, backward, and multi-point differencing, Richardson's extrapolation, Newton-Cotes rule, Romberg, and Gauss integration. 
<br>(4 weeks) Initial value problems for ordinary differential equations: Euler, Taylor, Runge-Kutta, variable step size, stability, convergence, stiffness.