4주: 선형 미분 방정식 시스템(Systems of linear differential equation)

[커세라] 이과생을 위한 미분 방정식(Differential Equations for Engineers)

0주: 환영(Welcome)
    W0.1 강좌 예고(Course Trailer)
    W0.2~5 강좌 개요(Course Overview)
    W0.6~7/1강 미분 방정식 소개 및 연습문제
                     (Introduction to Differential Equations & Practice Quiz)

1주: 1차 미분 방정식(Frst-order Differential Equation)
    W1.1/2강 수치해석:오일러 방법(Euler Method)
    W1.2/3강 1차 미분 방정식 세우기(Separable First-order equations)
    W1.3/4강 1차 미분 방정식 세우기 예제(Separable First-order equations:Example)
    W1.4 연습문제(Practice Quiz:Separable First-order ODEs)
    W1.5/5강 선형 1차 미분 방정식(Linear First-order Equations)
    W1.6/6강 선형 1차 미분 방정식:예제(Linear First-order Equations:Example)
    W1.7 연습문제(Practice Quiz:Linear First-Order ODE)
    W1.8/7강 선형 1차 미방 응용:예금(Application: Compound interest)
    W1.9/8강 선형 1차 미방 응용:종말속도(Application: Terminal Velocity)
    W1.10/9강 선형 1차 미방 응용:RC회로(Application: RC Circuit)
    W1.11 연습문제(Practice Quiz: Applications)
    W1.12 평가문제(Week-1 Graded Quiz)

2주: 2차 미분 방정식(Second-order Differential equations)
    W2.1/10강 고차 미분 방정식에 대한 오일러 방법(Euler method for higher-order odes)
    W2.2/11강 중첩의 원리(Principle of Superposition)
    W2.3/12강 론스키 행렬식(The Wronskian)
    W2.4/보강1 복소수(complex numbers)
    W2.5/13강 일원 2차 상미분 방정식(Homogeneous 2nd-order ODEs)
    W2.6/14강 예제1: 2개의 실근(Case1: Distinct Real Roots)
    W2.7/15강 예제2A: 켤레 복소수 근 A(Case 2: Complex-Conjugate Roots (Part A))
    W2.8/16강 예제2B: 켤레 복소수 근 B(Case 2: Complex-Conjugate Roots (Part B))
    W2.9/17강 예제3A: 중근 A(Case 3: Repeated Roots (Part A))
    W2.10/18강 예제3B: 중근 B(Case 3: Repeated Roots (Part B))
    W2.11 연습문제(Practice quiz: Homogeneous 2nd-order ODEs)
    W2.12/19강 이원 2차 상미분 방정식(Inhomogeneous 2nd-order ODEs)
    W2.13/20강 지수함수꼴 이원항(Inhomogeneous term:Exponential func.)
    W2.14/21강 삼각함수꼴 이원항(A)(Inhomogeneous term:sine or cosine-Part A)
    W2.15/22강 삼각함수꼴 이원항(B)(Inhomogeneous term:sine or cosine-Part B)
    W2.16/23강 다항함수꼴 이원항(Inhomogeneous term:Polynomials)
    W2.17/24강 공진현상(Resonance)
    W2.18 연습문제(Practice quiz: Inhomogeneous 2nd-order ODEs)
    W2.19/보강2 차원해석(Dimensional Analysis: Nondimensionalization)
    W2.20/25강 응용: RLC회로(Application: RLC Circuit)
    W2.21/26강 응용: 스프링에 달린 질량(Application: mass on a spring)
    W2.22/27강 응용: 진자운동(Application: Pendulum)
    W2.23/28강 응용: 감쇄공진(Application: Damped Resonance)
    W2.24 평가문제(Week-2 Graded Quiz)

3주: 라플라스 변환과 급수해(Laplace Transform and Series Solution)
    W3.1/29강 라플라스 변환의 정의(Definition of Laplace Transform)
    W3.2/30강 상미분 방정식의 라플라스 변환(Laplace transform of a const.coeff.ode)
    W3.3/31강 초기값 문제의 해(Solution of an Initial Value Problem)
    W3.4 연습문제:라플라스 변환(Practice Quiz: Laplace Transform)
    W3.5/32강 단위 계단함수(The heaviside step functions)
    W3.6/33강 디랙-델타 함수(The Dirac delta function)
    W3.7/34강 불연속 함수를 이원항으로 갖는 미분 방정식의 풀이
                   (solution of a discontinuous inhomogeneous term)
    W3.8/35강 임펄스 함수를 이원항으로 갖는 미분 방정식의 풀이
                   (Solution of an impulsive inhomogeneous term)
    W3.9 연습문제:불연속 및 임펄스 이원항
            (Practice Quiz: Discontinuous and Impulse Inhomogeneous Term)
    W3.10/36강 급수해법(The Series Solution Method)
    W3.11/37강 에어리 방정식의 급수해-A
                    (Series solution of the Airy's equation-Part A)
    W3.12/38강 에어리 방정식의 급수해-B
                    (Series solution of the Airy's equation-Part B)
    W3.13 연습문제:급수해(Practice Quiz: Series Solutions)

    W3.14 평가문제(Week-3 Grade Quiz)

4주: 선형 미분 방정식 시스템(Systems of linear differential equation)/동영상/영문자막



In this module, we'll learn how to solve coupled systems of linear differential equations.

These systems can be written as matrix equations, and are solved using eigenvalues and eigenvectors.

I'll then discuss the problem of normal modes, where coupled oscillators all vibrate at the same frequency.

We'll then solve the diffusion equation or partial differential equation.

To do this, we'll need to learn the basics of Fourier series. Please join me in this module of differential equations for engineers.