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
Overview
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）
