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Friday, November 19, 2010

Watched MIT 18.03 - lecture 13

I watched another lecture on differential equations by Prof. Arthur Matuck.

Lecture 13 is about finding solutions to the following ODE:
$y'' + Ay' + By = e^{\alpha x}$, with $\alpha$ a complex number.

The general solution is
$y = C_1 y_1 + C_2 y_2 + \frac{e^{\alpha x}} {\alpha^2 +A\alpha + B }$

where
$C_1 y_1 + C_2 y_2 = y_h$ is a solution the homogeneous part of the ODE and

$\frac{e^{\alpha x}}{\alpha^2 +A\alpha +B} = y_p$ is a particular solution of the ODE.

( I have not blogged about lectures 10,11 and 12 although I have seen them. Lectures 11 and 12 in particular were highly theoretical but did not add much in terms of new definitions or theorems.)

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Mathematics: is it the fabric of MEST?
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To create new theorems and proofs
To boldly go where no man has gone before

(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.)