Tuesday, February 27, 2007

Balbir's log - 27 Feb 2007

  1. Played around with Scilab, used scilab for some simple signal processing work, Amplitude Modulation.
  2. I've started reading a paper on VM entitled Making LRU friendly to weak locality workloads
  3. Added Markov chains to my to-learn list

Saturday, February 24, 2007

Using maxima -- baby steps

The use of symbolic computing makes it easy to visualize and solve problems that were otherwise dry and would put you to sleep. To test the simplicity of a freely available tool called maxima, I tried to solve a common problem with it.

The problem is quite simple, remember high school physics? Well I don't :-). Consider a tuning fork, which oscillates and produces a sound (depending on it's frequency).

We start by entering the mathematical model of the fork

'm*diff(x(t), t, 2)=-k*x(t);

Maxima prints


We now request maxima to solve the equation for us by

desolve([%],[x(t)]);

Maxima asks

Is k * m positive, negative, or zero? We say positive

Maxima prints



We ask maxima to simplify the result for us

radcan(%);

Maxima outputs



That's it, we have our solution.

Dynamic programming for the binomial coefficient

More fun things, this time with some visualisation of what happens when memoisation is used and what happens when we don't. I don'...