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Numerical Analysis

Princess Nora bint Abdul Rahman University via XuetangX

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Overview

This course is :

(1) to understand and explain how, why and when numerical approaches for solving methematical problems can be expected and worked;

(2)to provide a foundation for further study of scientific computations

Syllabus

[Week 1] 数值分析简介（수치해석학의 소개）

1. [Warming up]
2. [Lecture] 前言（들어가는 말）
3. [Lecture] What is Mathematics?
4. [Lecture] What is Numerical Analysis?
5. [Lecture] 数值分析的领域（수치해석의 영역）
6. [Activity] QUIZ

[Week 2] 非线性方程式（비선형 방정식）

1. [Warming up]
2. [Lecture] Introduction & Bisection Method
3. [Lecture] Fixed Point Iteration
4. [Lecture] Newton's Method
5. [Activity] QUIZ

[Week 3] Error Analysis

1. [Warming up]
2. [Lecture] Introduction & Bisection Method
3. [Lecture] Fixed Point Iteration
4. [Lecture] Newton's Method
5. [Activity] QUIZ

[Week 4] Interpolation

1. [Warming up]
2. [Lecture] Introduction & Lagrange Polynomial
3. [Lecture] Divided Difference
4. [Lecture] Binomial Theorem
5. [Lecture] Spline
6. [Activity] QUIZ

[Week 5] 积分，微分（적분, 미분）

1. [Warming up]
2. [Lecture] 积分，微分简介（적분, 미분 소개）
3. [Lecture] Newton Cotes Formula
4. [Lecture] Simpson's Rule
5. [Activity] QUIZ

[Week 6] Linear Algebra

1. [Warming up]
2. [Lecture] Polynomial Version
3. [Lecture] Matrix Version (Gauss Elimination)
4. [Lecture] Numerical Version
5. [Lecture] Determinant
6. [Lecture] Example
7. [Activity] QUIZ

[Week 7] LU Factorization

1. [Warming up]
2. [Lecture] LU Factorization
3. [Lecture] 计算方法（계산법）
4. [Lecture] Existence and Uniqueness
5. [Lecture] Cholesky Factorization
6. [Activity] QUIZ

[期中考试（중간고사）]

期中考试（중간고사）

[Week 8] QR Factorization

1. [Warming up]
2. [Lecture] Proof
3. [Lecture] Gram-Schmidt Process
4. [Lecture] Example
5. [Lecture] Matrix Norms
6. [Activity] QUIZ

[Week 9] Iterative Method

1. [Warming up]
2. [Lecture] Jacobi Iterative Method
3. [Lecture] Gauss Seidel Iterative Method
4. [Lecture] Convergence Theorem
5. [Lecture] Example
6. [Activity] QUIZ

[Week 10] Positive Definite

1. [Warming up]
2. [Lecture] Definition
3. [Lecture] Theorem & Example 1
4. [Lecture] Theorem & Example 2
5. [Lecture] Theorem & Example 3
6. [Lecture] Theorem & Example 4
7. [Activity] QUIZ

[Week 11] Ordinary Differential Equation

1. [Warming up]
2. [Lecture] First Order Equation
3. [Lecture] Euler's Method
4. [Lecture] Error Analysis
5. [Lecture] Euler Method
6. [Activity] QUIZ

[Week 12] Runge-Kutta Methods

1. [Warming up]
1. [Lecture] Introduction
2. [Lecture] n-th Runge-Kutta Methods
3. [Lecture] Multi Step Method
4. [Lecture] Explicit
5. [Lecture] Example
QUIZ

[Week 13] O.D.E. and P.D.E.

1. [Warming up]
2. [Lecture] Boundary Value Problem With O.D.E.
3. [Lecture] Partial Differential Equations
4. [Activity] QUIZ

[期末考试（기말고사]

期末考试（기말고사）

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