數值方法

臺北科技大學 115-1 學期課程，課號 363516。

課程大綱

This course teaches the basic theory of numerical methods to apply numerical algorithms in solving various types of mathematical problems by using a computer. The content includes error analysis and problem-solving of nonlinear equation (bisection, Newton, secant method), linear and nonlinear systems, curve fitting ( regression, Lagrange interpolation, spline curve), numerical differentiation and integration, ordinary differential equation, optimization, etc.

課程進度

wk1: Introduction to MS Excel & VBA; Bracketing Methods for Locating a Root wk2: Newton-Raphson and Secant Methods wk3: Review of Taylor Series; Number Representation; Number Representation and Errors; Error Analysis wk4: Interpolation and Lagrange Approximation wk5: Quiz wk6: Numerical Differentiation Formulas wk7: Numerical Integration wk8: Double Integral Method wk9: Midterm Exam. wk10: Gaussian Elimination wk11: LU Decomposition, Pivoting, and Triangular Factorization wk12: Curve Fitting and Least Squares Method wk13: Interpolation by Spline Function wk14: Unconstrained Optimization wk15: Optimization by the Heuristic Search Method wk16: Final Exam. wk17: Solving Ordinary Differential Equations (Flexible Learning) wk18: Constrained Optimization (Flexible Learning)

評量方式

1. Homework*5(50%) 2. Quiz*1 (10%) 3. Midterm & Final (40%)

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 1. Numerical Methods for Engineers, Chapra & Canale, McGraw Hill. 2. Numerical Methods Using MATLAB, Jhon. & Kurtis. 3. Handouts