gibson:teaching:fall-2014:math445:lecture10-diary

The following example problem spells out in great detail how to translate a formula in summation notation into a Matlab `for`

loop.

Recall this classic formula for due to Euler:

We can sum the first N terms of this series with the Matlab one-liner

N=100; sum((1:N).^(-2))

We can also do the sum with a `for`

loop. To see how to build the `for`

loop, it's helpful to think of the series as a sequence of *partial sums*

etc. Note that the difference between successive partial sums is a single term.

So we can compute the th partial sum by successively adding the term for n going from 1 to N.

That's exactly we do when we compute the sum with a `for`

loop.

N=100; P=0; for n=1:N P = P + 1/n^2; end

At each step in the `for`

loop, we compute for the current value of , add it to the previously computed partial sum , and then store the result into . But, since we are only interested in the final value , we just store the current value of the partial sum in the variable P and write over it with the next value each time we step through the loop.

gibson/teaching/fall-2014/math445/lecture10-diary.txt · Last modified: 2014/10/17 10:23 by gibson