W2.6/14강 예제1: 2개의 실근(Case1: Distinct Real Roots)

[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 with constant coefficients)

W2.6/14강 예제1: 2개의 실근(Case1: Distinct Real Roots)/동영상/영문자막

We're solving the second order, a homogeneous differential equation with constant coefficients,

trying to satisfy two initial conditions,

We use our 'ansatz',

Get our characteristic equation,

In this case, the factors, and we have two distinct real roots.

(인수분해로 가볍게 두개의 근을 찾아내자)

We use the principle of superposition to write the general solution.

가설풀이 방법으로 얻은 두개의 (특수)해에 대하여 중첩의 원리를 적용하여 일반해를 구한다.

We need the time derivative of that,

Then, we satisfy the two initial conditions,

that gives us two linear equations for the two unknowns, c1 and c2,

and then we can find the specific solution that satisfies both the differential equation and the initial conditions.

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