Mathematics

This is a common question on mathematical discussion boards, with people sometimes feeling that mathematicians are too closed-minded for (...)

This article contains an elementary introduction to calculus of finite differences. Instead of working with a variable, say $n$, it uses a (...)

In the previous article, we discussed how to integrate functions without using variables, but only in the case of indefinite integration. (...)

I have written several articles about a way to do classical calculus without using variables, e.g. how to differentiate or integrate (...)

This article is based on my article about integration without variables which you may want to read first in order to understand what’s (...)

In this article, I’ll assume you have already read my article on differentiation without variables. Just as a quick reminder: $\iota$ (...)

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 (...)

Let’s face it—mathematical expressions rendered as images look ugly, especially in inline formulas. Also, if you, like me, have all (...)

To be able to differentiate a function without using variables, we have to be able to denote the function we want to differentiate without (...)

First, note that this article is not about the definition of elementary functions, such as $\sin$ and $\cos$, and operations, like $a^b$, (...)