MATH 3230 數值分析 Numerical Analysis

Course Code	MATH 3230 MATH3230			科目名稱		Numerical Analysis 數值分析
教員	Professor ZOU Jun  [官方介紹] [學術著作]			學　　分		3學分
課程性質				同科其他選擇
Workload	l   非PAPER類HOMEWORK l   TUTORIAL / PRESENTATION l   MIDTERM l   FINAL EXAM								好重	1
									重
									平均
									輕
									極輕
評價教學內容	#1 不有趣
評價教員教學	#1 1999，教得好差
CUSIS科目資料	Description： Floating-point numbers and roundoff errors, absolute and relative errors, stable and unstable computations, solutions of nonlinear equations, linear systems, interpolation, numerical differentiation, and numerical integration. Students taking this course are expected to have knowledge in advanced calculus and linear algebra.   Learning Outcome： Students are expected to understand the fundamental concepts involved in numerical analysis, and learn some basic approaches and techniques in solving linear and nonlinear systems, constructing interpolations and do numerical differntiation and integration. The basic learning outcomes include:   - Students understand the basic concepts in scientific computings, including fixed-point numbers, floating-point numbers, single and double precision, overflow and underflow, roundoff errors, absolute and relative errors, stable and unstable computations.   - Students learn some basic knowledge in floating-point arithmetic and know how to use the backward error analysis to estimate possible errors generated in numerical computings.   - Students learn some basic concepts in solving nonlinear equations of one variable: iterative methods, rate of convergence, local and global convergence; learn some classical methods for solving nonlinear equations of one variable: bisection methods, Newton's method, quasi-Newton's method and fixed-point iteration, and learn how to analyse convergence of these method.   - Students learn some basic methods for solving linear system of equations: Cholesky factorization, LU and LDU factorization, forward- and backward-substitutions for traingular systems, Gaussian elimination.   - Students learn sensitivity analysis of the solutions of linear systems with respect to some errors in their coefficient matrices or in their right-hand sides, and understand condition numbers and their importance.   - Students learn three polynomial interpolations, Newton form of interpolations, Lagrange and spline interpolations, and learn how to estimate the interpolation errors.   - Students learn some popular numerical integrations: trapezoidal and composite trapezoidal rules, Simpson and composite Simpson rules, Newton-Cotes quadrature rule, Gaussian quadrature rules, and learn how to estimate the errors of quadrature rules.   - Students learn some basic numerical differentiation techniques: forward differences, backward differences, central differences, and understand how to estimate the errors of these difference schemes.
其他資料	2019Sem1：學位 70|註冊 49|剩餘 21
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