Posts Tagged ‘method’
Method NO. 3 : Neat Integral
16Sep08
Today, I decided to post a very eye-catching method for calculating an integral which shows very often in Statistical Mechanics in Physics.
Let’s try to calc this
First let’s mark it with a name , then
What is just a double integral over the whole 2d surface. It can be also written in polar coordinate system as [...]
Filed under: Mathematics, Methods | 7 Comments
Tags: coordinate, integral, math, method, pi, polar
Lets calculate more compilated sum
further, the last one equals to and now the first of the sums is equal to however the second one is easy, cause its a geometric sequence equal to under the law from previous post. Now we have , in the result of elementary algebraic transformation we [...]
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Tags: math, method, sequence, sum, upset, upseting
Asume that we want to calculate
Of course,
But the sum on the right side is equal to Therefore and so,
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Tags: geometric, math, method, sequence, sum
