# Mathematics

 Calculus of finite differences without variables This article contains an elementary introduction to calculus of finite differences. Instead of working with a variable, say $n$, it uses a (...) May 8, 2014 – Jakub Marian – Mathematics
 Definite integration without variables In the previous article, we discussed how to integrate functions without using variables, but only in the case of indefinite integration. (...) April 23, 2014 – Jakub Marian – Mathematics
 Quantification without variables I have written several articles about a way to do classical calculus without using variables, e.g. how to differentiate or integrate (...) February 15, 2014 – Jakub Marian – Mathematics
 Second substitution method for integration without variables This article is based on my article about integration without variables which you may want to read first in order to understand what’s (...) February 1, 2014 – Jakub Marian – Mathematics
 Indefinite integration without variables In this article, I’ll assume you have already read my article on differentiation without variables. Just as a quick reminder: $\iota$ (...) January 12, 2014 – Jakub Marian – Mathematics

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 Integral of $\cos^2(x)$ Let’s use integration by parts: If we apply integration by parts to the rightmost expression again, we will get $∫\cos^2(x)dx = ∫\cos^2(x)dx$, which is not very useful. The trick is to rewrite the $\sin^2(x)$ in the second step as $1-\cos^2(x)$. Then we get (...) November 24, 2013 – Jakub Marian – Mathematics
 How to define functions without using variables First, note that this article is not about the definition of elementary functions, such as $\sin$ and $\cos$, and operations, like $a^b$, (...) October 11, 2013 – Jakub Marian – Mathematics