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## Wednesday, November 24, 2010

### Watched MIT 18.02 - Lecture 8

A lecture in which Prof. Denis Auroux says: "Applied mathematics is physics with a different set of symbols." To the math.

Lecture 8 starts a new unit in the 18.02 series and is about functions of several variables, the graph of a function of two variables, contour plots of functions of two variables and partial derivatives.

The image above shows the graph and the contour plot of $f(x,y)=1-(x^2+y^2)$ followed by the partial derivatives as calculated by Mathematica.

Partial derivatives are defined as follows:
$$\frac{\partial f}{\partial x}(x,y) = \displaystyle\lim_{\Delta x \to 0}\frac{f(x+\Delta x, y) - f(x,y)}{\Delta x}$$
$$\frac{\partial f}{\partial y}(x,y) = \displaystyle\lim_{\Delta y \to 0}\frac{f(x, y+\Delta y) - f(x,y)}{\Delta y}$$

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## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
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.)