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非線性方程式的根、高維度非線性方程式的根
[自學課程]數值分析Numerical Analysis
第一週：數值分析課程簡介、數值誤差的來源
Week1 Unit0 電腦的暴力
Week1 Unit1 授課方式介紹
Week1 Unit2 數值誤差的來源
Week1 Unit3 Python程式簡介
Week1 Unit4 數值誤差的來源
第一週測驗
第二週：基礎Python 程式入門
Week2 Unit0 Python程式安裝教學
Week2 Unit1 Python初步入門
Week2 Unit2 Python 常用的型別
Week2 Unit3 Python 流程控制
Week2 Unit4 Python 模組引用與常用函數
Week2 Unit5 Python 函數的定義方式
Week2 Unit6 Python 檔案的操作
Week2 Unit7 Python 繪圖
基礎Python 程式入門
第三週：非線性方程式的根、高維度非線性方程式的根
Week3 Unit00 Newton Method
Week3 Unit01 Genetic method
Week3 Unit02 Bisection method
Week3 Unit03 Simple iteration and python
Week3 Unit04 brouwer's fixed point theorem
Week3 Unit05 constraction mapping
Week3 Unit06 Newton's method
Week3 Unit07 Recall Newton's method
Week3 Unit08 newton's method 2nd convergence
Week3 Unit09 big O
Week3 Unit10 Mooc's 收斂速度定義
Week3 Unit11 Secant Method
非線性方程式的根、高維度非線性方程式的根
第四週：求解線性方程組
Week4 Unit0 當週課程介紹
Week4 Unit1 矩陣與線性方程組
Week4 Unit2 row operation
Week4 Unit3 Gauss elimination
Week4 Unit4 LU decomposition
Week4 Unit5 solving triangular system
求解線性方程組
第五週：正交化與特徵值
Week5 Unit0 當週課程介紹
Week5 Unit1 inverse power method
Week5 Unit2 Power method
Week5 Unit3 Orthogonalization of vectors
Week5 Unit4 Gram Schmidt
Week5 Unit5 QR Decomposition
正交化與特徵值
第六週：插值法
Week6 Unit0 當週課程介紹
Week6 Unit1 introduction to interpolation
Week6 Unit2 Lagrange interpolation
Week6 Unit3 Hermite interpolation
Week6 Unit4 Neville's algorithm
Week6 Unit5 basis of polynomial
Week6 Unit6 uniqueness of polynomial interpolation
Week6 Unit7 Newton interpolation
Week6 Unit8 B spline
插值法
第七週：數值微分
Week7 Unit0 當週課程介紹
Week7 Unit 1 數值微分：Forward, backward and central method
Week7 Unit 2 Richardson extrapolation
Week7 Unit 3 effect of rounding error
Week7 Unit 4 high order differential
第八週：數值積分
Week8 Unit0 當週課程介紹
Week8 Unit1 中點法，梯形法和辛普森法
Week8 Unit2 數值積分誤差分析
Week8 Unit3 adaptive quadrature
Week8 Unit4 Gauss quadrature
第九週：數值微分方程
Week9 Unit0 當週課程介紹
Week9 Unit1 Euler Method
Week9 Unit2 Heun's method
Week9 Unit3 Runge Kutta method
Week9 Unit4 shooting method
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Week3 Unit11 Secant Method
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第四週：求解線性方程組