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Monday, November 8, 2010

Watched MIT 18.03 - lecture 9

I skipped lectures 7,8 (watched 7 partially and had a brief look at 8 ) because during this first serious confrontation with differential equations I want to follow the route of MST209 ( OpenLearn version ).

In 18.03 lecture 9 Prof. Mattuck talks about differential equations of type $y'' + Ay' + By = 0$. They are of the 2nd order, have constant coefficients and are homogeneous. The procedure for solving them is surprisingly similar to solving second order recurrence equations. The DE has a characteristic equation $r^2 + Ar + B=0$. If both roots are real and distinct the general solution then looks like $y=c_1 \cdot e^{r_1x} + c_2 \cdot e^{r_2x}$. The other two cases ( i.e. a pair of complex conjugates, two real equal roots ) are discussed during the rest of the lecture.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)