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 MarianMathematics
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 MarianMathematics
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 MarianMathematics
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 MarianMathematics
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 MarianMathematics

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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 MarianMathematics
Render LaTeX in Wikipedia using Mathjax
Let’s face itmathematical expressions rendered as images look ugly, especially in inline formulas. Also, if you, like me, have all (...)
October 26, 2013 – Jakub MarianBlog, Mathematics
Differentiation (derivatives) without variables
To be able to differentiate a function without using variables, we have to be able to denote the function we want to differentiate without (...)
October 14, 2013 – Jakub MarianMathematics
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 MarianMathematics
Applying an operator with respect to a variable
There are seemingly two kinds of “operations” used in mathematics when it comes to working with functions; you can either take a function (...)
October 10, 2013 – Jakub MarianMathematics