蕭百沂教授 09610 ESS 305001 數值分析一(Numerical Analysis I)
<br>課程大綱： 
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<br>一、課程說明(Course Description) 
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<br>As having been stated in the preface of the text book, 
<br>the purpose of this course is 
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<br>"to introduce morden approximation techniques; 
<br>to explain how, why, and when they can be expected to work; and 
<br>to provide a foundation for further study of numerical analysis and 
<br>scientific computing" 
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<br>二、指定用書(Text Books) 
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<br>Burden and Faires, Numerical Analysis, 8th ed. (Thomson 2005) 
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<br>三、參考書籍(References) 
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<br>N/A 
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<br>四、教學方式(Teaching Method) 
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<br>Three-hour lectures per week 
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<br>五、教學進度(Syllabus) 
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<br>1. Chap 1: (week 1) IEEE Standard 754,  error analysis
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<br>2. Chap 2: (week 2&3) Root finding & fixed-point problems: bisection method, Newton's method, secant method, method of false position, Mueller's method, Modified Newton's method,   order of convergence, Aitken's method, Steffensen's method [, zeros of polynomials, horner's method]
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<br>3. Chap3 : (week 4&5&6) Lagrange interpolation, Neville's method, Newton's divided-Difference (forward, backward), [Stirling's formula], Hermit interpolation, natural and clamped cubic spline interpolation, [parametric curves] 
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<br>4. Chap 6 : (week 7&8) Gaussian elimination and backward substitution, pivoting strategies, matrix inversion, determinant, LU factorization (Dolittle, Crout, Cholesky), LDLt Factorization, LLt Factorization.
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<br>5. Chap 4 : (week 9&10&11)  (n+1)-point formula to approximate first order derivative, Richardson's extrapolation, Trapezoidal rule and Simposon's rule for integration, composite method for integration, Romberg integration, adaptive quadrature method, Gaussian quadrature, multiple integrals, improper integrals. 
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<br>6. Chap 5: (week 12&13&14) Euler's method, higher-order Taylor method, Runge-Kutta method, Multistep methods (Adams-Bashforth, Adams-Moulton), Higher-order equations and systems of differential equations
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<br>7. Chap 11:(week 15&16) Shooting method (nonlinear, linear), finite-difference method for linear problem.
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<br>六、成績考核(Evaluation) 
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<br>Homeworks 30%, Midterm exam 30%, Final exam 40%
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<br>七、可連結之網頁位址 
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<br>N/A  
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