Articles · Kostas Maistrelis

Logistic Population Growth — When Space Starts to Matter

Kostas Maistrelis — Wed, 01 Jul 2026 20:28:04 +0300

From the exponential to the logistic equation: how the carrying capacity K of the environment turns unchecked growth into a sigmoidal curve. A standalone R Markdown lesson with qualitative analysis, phase portrait, numerical solution (deSolve) and parameter estimation.

Exponential Population Growth — From Water Lilies to the Differential Equation

Kostas Maistrelis — Wed, 01 Jul 2026 18:00:00 +0300

How, starting from a simple observation — a 10% daily increase in the water lilies of a lake — we arrive at the exponential growth formula by way of a differential equation. A standalone R Markdown lesson with text, R code, plots and mathematics.

Introduction to Derivatives — A Car on the Road

Kostas Maistrelis — Tue, 30 Jun 2026 18:07:48 +0300

A short introduction/reminder to the concept of the derivative — the «rate of change». Each lesson opens as a standalone page (R Markdown).

The Normal Distribution and its origin

Kostas Maistrelis — Mon, 23 Feb 2015 21:32:16 +0200

Quite a few statistics and probability textbooks with an introduction to the normal distribution have passed through my hands. They almost always started with the mathematical definition and moved on to the properties and uses of the distribution. For a long time I had not found a book that explained how this formula came about — until at some point a book called Lady Luck fell into my hands which, although old, is a very good introduction to the subject of probability, and in it I found the first clear description of how the normal distribution arises.