Archive for the ‘Methods’ Category

The polynomial argument is a very useful fact which can be used in order to prove, or justify a statement. It bases on simple fact that non-zero polynomial of k degree, can have no more than k solutions, futhermore the¬†difference of two polynomials of k degree can also have max of k solutions if only […]

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 […]

Suppose that we have a grounded sphere made from a conductor and an electron far from the sphere. Let the radius of the sphere be and the beginning speed of the electron be orientated on the line in distance of from the center of the sphere. The smallest distance between electron and the center of […]

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 recieve It’s easy […]

Asume that we want to calculate Of course, But the sum on the right side is equal to Therefore and so,