SKKU Engineering Math Labs
[Sage Reference]
http://matrix.skku.ac.kr/2010-Album/Sage-QReference-SKKU.pdf
Engineering Mathematics 1
(1st semester)
Week 1 http://matrix.skku.ac.kr/2020-EM/EM-1-W1/EM-1-W1-Lab.html
1.1: Basic Concepts, Modeling
3.1 1계 미분방정식의 개념
1.3: Separable ODEs, Modeling
3.2 변수분리형 미분방정식
1.4: Exact ODEs
3.3 완전미분방정식
http://www.hanbit.co.kr/EM/sage/1_chap3.html
Week 2 http://matrix.skku.ac.kr/2020-EM/EM-1-W2/EM-1-W2-Lab.html
1.4: Integrating Factors
3.4 적분인자
http://www.hanbit.co.kr/EM/sage/1_chap3.html
1.5: Linear ODEs, Bernoulli Equation
3.5 선형미분방정식
Week 3 http://matrix.skku.ac.kr/2020-EM/EM-1-W3/EM-1-W3-Lab.html
2.1: Homogeneous Linear ODEs of 2nd Order
4.1 2계 선형미분방정식의 개념
2.2: Homogeneous Linear ODEs with Constant Coefficients
4.2 상수 계수 동차선형미분방정식
2.5: Euler Cauchy Equations
4.3 오일러-코시 방정식
http://www.hanbit.co.kr/EM/sage/1_chap4.html
Week 4 http://matrix.skku.ac.kr/2020-EM/EM-1-W4/EM-1-W4-Lab.html
2.6: Existence and Uniqueness of Solutions. Wronskian
2.7: Nonhomogeneous ODEs
4.4 비동차 선형미분방정식
3.6 매개변수변화법(1계)
http://www.hanbit.co.kr/EM/sage/1_chap4.html
Week 5 http://matrix.skku.ac.kr/2020-EM/EM-1-W5/EM-1-W5-Lab.html
2.10: Solution by Variation of Parameters
4.5 매개변수변화법(2계)
http://www.hanbit.co.kr/EM/sage/1_chap4.html
4.1: Systems of ODEs as Models in Engineering Applications
5.1. Power Series Method
Week 6 http://matrix.skku.ac.kr/2020-EM/EM-1-W6/EM-1-W6-Lab.html
5.2: Legendre's Equation. Legendre Polynomials
7.4 르장드르 방정식
5.3: Extended Power Series Method: Frobenius Method
7.2 급수해법
7.3 프로베니우스 해법
http://www.hanbit.co.kr/EM/sage/1_chap7.html
Week 7 http://matrix.skku.ac.kr/2020-EM/EM-1-W7/EM-1-W7-Lab.html
5.4 Bessel’s Equation. Bessel Functions
5.5 Bessel Functions of the 
. General Solution
7.5 베셀 방정식
http://www.hanbit.co.kr/EM/sage/1_chap7.html
Week 8
Review and Project proposal (presentation)
복습, 프로젝트(과제) 제안서 발표
Midterm Exam
Week 9 http://matrix.skku.ac.kr/2020-EM/EM-1-W9/EM-1-W9-Lab.html
6.1: Laplace Transform, Linearity, First Shifting Theorem
8.1 라플라스 변환의 도입
http://www.hanbit.co.kr/EM/sage/1_chap8.html
6.2: Transforms of Derivatives and Integrals
8.2 라플라스 변환의 정의와 특성
6.3: Unit Step Function, t-shifting
http://www.hanbit.co.kr/EM/sage/1_chap8.html
Week 10 http://matrix.skku.ac.kr/2020-EM/EM-1-W10/EM-1-W10-Lab.html
6.4: Short Impulses, Dirac’s Delta Function
6.5: Convolution. Integral Equations
6.6: Differentiation and Integration of Transforms. ODEs with Variable Coefficients
8.3 라플라스 변환을 이용한 미분방정식의 풀이
8.4, 8.5 라플라스 변환의 응용
http://www.hanbit.co.kr/EM/sage/1_chap8.html
Week 11 http://matrix.skku.ac.kr/2020-EM/EM-1-W11/EM-1-W11-Lab.html
6.7: Systems of ODEs
6.1 연립미분방정식이란
6.2 동차 선형연립미분방정식
6.4 기본행렬과 지수행렬을 이용한 연립미분방정식의 풀이
6.6 연립미분방정식의 분리
http://www.hanbit.co.kr/EM/sage/1_chap6.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W7-lab.html
7.1: Matrices, Vectors
1.1 행렬의 성질과 연산
http://matrix.skku.ac.kr/LA/Ch-3/
7.2: Matrix Multiplication
1.1 행렬의 성질과 연산
http://matrix.skku.ac.kr/LA/Ch-3/
Week 12 http://matrix.skku.ac.kr/2020-EM/EM-1-W12/EM-1-W12-Lab.html
7.3: Linear Systems of Equations
1.2 선형연립방정식
http://matrix.skku.ac.kr/LA/Ch-2/
7.4: Linear Independence, Rank of Matrix, Vector Space
1.3 일차독립과 일차종속, 계수
http://www.hanbit.co.kr/EM/sage/1_chap1.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W5-lab.html
7.5: Solutions of Linear Systems
Week 13 http://matrix.skku.ac.kr/2020-EM/EM-1-W13/EM-1-W13-Lab.html
7.6: For Reference: Second and Third-Order Determinants
1.4 행렬식과 여인자 전개
http://matrix.skku.ac.kr/LA/Ch-4/
http://www.hanbit.co.kr/EM/sage/1_chap1.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W5-lab.html
7.7: Determinants.
1.4 행렬식과 여인자 전개
http://matrix.skku.ac.kr/LA/Ch-4/
7.8: Inverse of Matrix
1.5 역행렬과 크래머 법칙
http://matrix.skku.ac.kr/LA/Ch-4/
http://www.hanbit.co.kr/EM/sage/1_chap1.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W5-lab.html
Week 14 http://matrix.skku.ac.kr/2020-EM/EM-1-W14/EM-1-W14-Lab.html
8.1: The Matrix Eigenvalue Problem
1.6 고유값과 고유벡터
http://matrix.skku.ac.kr/LA/Ch-4/
8.2: Some Applications of Eigenvalue Problems
1.7 닮음, 행렬의 대각화, 이차형식
http://matrix.skku.ac.kr/LA/Ch-8/
http://matrix.skku.ac.kr/2018-EM/EM-2-W6-lab.html
Week 15 http://matrix.skku.ac.kr/2020-EM/EM-1-W15/EM-1-W15-Lab.html
8.3: Symmetric, Skew-Symmetric, and Orthogonal Matrix
8.4: Eigenbases, Diagonalization, Quadratic Forms
1.7 닮음, 행렬의 대각화, 이차형식
http://matrix.skku.ac.kr/LA/Ch-8/
http://www.hanbit.co.kr/EM/sage/1_chap1.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W6-lab.html
Week 16
Review and Project / Homework presentation
복습, 프로젝트(과제) 발표
Final Exam
Copyright @ 2020 SKKU Matrix Lab. All rights reserved.
Made by Manager: Prof. Sang-Gu Lee and Dr. Jae Hwa Lee
*This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03035865).
