[ 공학수학 1, 2 ]
[한빛 아카데미] Engineering Mathematics with Sage:
[저자] 이상구, 김영록, 박준현, 김응기, 이재화
About this Lab for Engineering Mathematics (강의록과 실습실):
http://matrix.skku.ac.kr/2020-EM/EM-1-Labs.htm
http://matrix.skku.ac.kr/2019-EM/EM-2-Labs.htm (SGLee)
by Sang-Gu Lee with J.H. Lee & E.-k. Kim
Contents
A. 공학수학 1 – 선형대수, 상미분방정식+ Lab
Chapter 00 서문 http://matrix.skku.ac.kr/EM-Sage/Preface.html
Chapter 01 벡터와 선형대수
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-1.html
Chapter 02 미분방정식의 이해
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-2.html
Chapter 03 1계 상미분방정식
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-3.html
Chapter 04 2계 상미분방정식
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-4.html
Chapter 05 고계 상미분방정식
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-5.html
Chapter 06 연립미분방정식, 비선형미분방정식
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-6.html
Chapter 07 상미분방정식의 급수해법, 특수함수
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-7.html
Chapter 08 라플라스 변환
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-8.html
B. 공학수학 2 - 벡터미적분, 복소해석 + Lab
Chapter 09 벡터미분, 기울기, 발산, 회전
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-9.html
Chapter 10 벡터적분, 적분정리
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-10.html
Chapter 11 푸리에 급수, 적분 및 변환
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-11.html
Chapter 12 편미분방정식
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-12.html
Chapter 13 복소수와 복소함수, 복소미분
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-13.html
Chapter 14 복소적분
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-14.html
Chapter 15 급수, 유수
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-15.html
Chapter 16 등각사상
http://matrix.skku.ac.kr/EM-Sage/E-Math-Chapter-16.html
Appendix http://matrix.skku.ac.kr/EM-Sage/Appen.html
[ SKKU 반도체 공학과 공학수학 1, 2 <실습실> ]
Engineering Mathematics 1 (1 학기)
[Sage Reference]
http://matrix.skku.ac.kr/2010-Album/Sage-QReference-SKKU.pdf
http://matrix.skku.ac.kr/2014-DE-0/Engineering_Math-Sample-New.htm
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
[ SKKU Engineering Math 2. ]
(2nd semester)
Week 1 http://matrix.skku.ac.kr/2019-EM/EM-2-W1/EM-2-W1-Lab.htm
11.1: Fourier Series
11.1 푸리에 급수란
11.2: Arbitrary Period
11.2 푸리에 급수와 경계조건
http://www.hanbit.co.kr/EM/sage/2_chap11.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W1-lab.html
Week 2 http://matrix.skku.ac.kr/2019-EM/EM-2-W2/EM-2-W2-Lab.htm
11.2: Even and Odd Functions. Half-Range Expansions
11.3 푸리에 급수의 기하학적 접근
11.7: Fourier Integral
http://www.hanbit.co.kr/EM/sage/2_chap11.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W2-lab.html
Week 3 http://matrix.skku.ac.kr/2019-EM/EM-2-W3/EM-2-W3-Lab.htm
11.8: Fourier Cosine and Sine Transforms
11.4 푸리에 급수의 수렴
*11.5 스투룹-리우빌 정리와 직교함수
11.9: Fourier Transform
11.6 푸리에 변환
http://www.hanbit.co.kr/EM/sage/2_chap11.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W3-lab.html
Week 4 http://matrix.skku.ac.kr/2019-EM/EM-2-W4/EM-2-W4-Lab.htm
12.1: Basic Concepts of PDEs
12.1 편미분방정식이란
12.2: Modeling: Wave Equation
http://www.hanbit.co.kr/EM/sage/2_chap12.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W4-lab.html
Week 5 http://matrix.skku.ac.kr/2019-EM/EM-2-W5/EM-2-W5-Lab.htm
12.3: Solution by Separating Variables. Use of Fourier Series
12.5: Modeling: Heat Equation
12.3 파동방정식
12.6: Heat Equation: Solution by Fourier Series.
12.4 확산방정식
http://www.hanbit.co.kr/EM/sage/2_chap12.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W4-lab.html
Week 6 http://matrix.skku.ac.kr/2019-EM/EM-2-W6/EM-2-W6-Lab.htm
12.6: Heat Equation: Steady Two-Dimensional Heat Problems. Dirichlet Problem
12.4 확산방정식
12.7: Heat Equation: Solution by Fourier Integrals and Transforms
http://www.hanbit.co.kr/EM/sage/2_chap12.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W4-lab.html
Week 7 http://matrix.skku.ac.kr/2019-EM/EM-2-W7/EM-2-W7-Lab.htm
13.1: Complex Numbers.
13.2: Polar Form of Complex Numbers. Powers and Roots
13.1 복소수
13.2 복소함수
http://www.hanbit.co.kr/EM/sage/2_chap13.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W9-lab.html
Week 8
Review and Project proposal (presentation)
복습, 프로젝트(과제) 제안서 발표
Midterm Exam
Week 9 http://matrix.skku.ac.kr/2019-EM/EM-2-W9/EM-2-W9-Lab.htm
13.3: Derivative. Analytic Function
13.1 복소수
13.2 복소함수
13.4: Cauchy–Riemann Equations. Laplace’s Equation
13.3 코시-리만방정식
13.5: Exponential Functions
13.4 복소 지수함수와 복소 로그함수
http://www.hanbit.co.kr/EM/sage/2_chap13.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W9-lab.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W10-lab.html
Week 10 http://matrix.skku.ac.kr/2019-EM/EM-2-W10/EM-2-W10-Lab.htm
13.6.: Trigonometric and Hyperbolic Functions. Euler’s Formula
13.5 복소 삼각함수와 복소 쌍곡함수
13.7: Logarithm. General Power. Principal Value
http://www.hanbit.co.kr/EM/sage/2_chap13.html
Week 11 http://matrix.skku.ac.kr/2019-EM/EM-2-W11/EM-2-W11-Lab.htm
14.1: Line Integral in the Complex Plane
14.1 복소평면에서의 선적분
14.2: Cauchy’s Integral Theorem
14.2 코시-구르사 정리
*14.3: Cauchy’s Integral Formula
14.3 코시 적분 공식
*14.4: Derivatives of Analytic Functions
http://www.hanbit.co.kr/EM/sage/2_chap14.html
Week 12 http://matrix.skku.ac.kr/2019-EM/EM-2-W12/EM-2-W12-Lab.htm
*15.1: Sequences, Series, Convergence Tests
*15.2: Power Series
*15.3: Functions Given by Power Series
15.1 복소 수열과 복소 무한급수
15.4: Taylor and Maclaurin Series
15.2 테일러 급수와 로랑급수
http://www.hanbit.co.kr/EM/sage/2_chap14.html
Week 13 http://matrix.skku.ac.kr/2019-EM/EM-2-W13/EM-2-W13-Lab.htm
24.1: Data Representation. Average. Spread
24.2: Experiments, Outcomes, Events
24.3: Probability
http://matrix.skku.ac.kr/2018-album/R-Sage-Stat-Lab-1.html
Week 14 http://matrix.skku.ac.kr/2019-EM/EM-2-W14/EM-2-W14-Lab.htm
24.4: Permutations and Combinations
(New) Conditional Probability and Independence, Bayes' theorem
24.5: Random Variables. Probability Distributions
24.6: Mean and Variance of a Distribution
http://matrix.skku.ac.kr/2018-album/R-Sage-Stat-Lab-1.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W11-lab.html
Week 15 http://matrix.skku.ac.kr/2019-EM/EM-2-W15/EM-2-W15-Lab.htm
24.7: Binomial, Poisson, and Hypergeometric Distributions
http://matrix.skku.ac.kr/2018-album/R-Sage-Stat-Lab-2.html
24.8: Normal Distribution
http://matrix.skku.ac.kr/2018-album/R-Sage-Stat-Lab-2.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W12-lab.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W13-lab.html
http://matrix.skku.ac.kr/2018-EM/EM-2-W14-lab.html
인공지능을 위한 기초수학 18강 (통계 1: 통계학과 R), Basic Math for AI 18 https://youtu.be/u82BC1RiJ0A
인공지능을 위한 기초수학 19강 (통계 2: 순열, 조합, 확률), Basic Math for AI 19 https://youtu.be/KQXO-XbJauU
인공지능을 위한 기초수학 20강 (통계 3: 확률변수), Basic Math for AI 20 https://youtu.be/SUsZHarQqqg
인공지능을 위한 기초수학 21강 (통계 4: 이산확률분포), Basic Math for AI 21 https://youtu.be/Fq7D7bGG_cE
인공지능을 위한 기초수학 22강 (통계 5: 연속확률분포), Basic Math for AI 22 https://youtu.be/4wx1raETI8o
인공지능을 위한 기초수학 23강 (통계 6: 공분산과 상관계수, 데이터 활용의 실제), Basic Math for AI 23 https://youtu.be/oUSPhkyEWp4 (50:05)
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 & 김응 기 http://matrix.skku.ac.kr/sglee/
*This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03035865)
