A short introduction/reminder to the concept of the derivative — the «rate of change». Each lesson opens as a standalone page (R Markdown: text, R code, plots and mathematics).
Part 1 — What does «rate of change» mean?
Taking a car on the road as a starting point: how position, speed and acceleration are connected. The lesson proceeds step by step — defining time, speed, distance, acceleration, plots, instantaneous speed — and closes with the connection to biology.
Part of the series: Population Dynamics — From the Derivative to the Logistic Equation
Preview — click for the full lesson →
Part 2 — The Derivative as the Slope of the Tangent
From the «rate of change» to geometry: the derivative as the slope of the tangent at a point. For \(y = x^2\) the derivative is \(\frac{dy}{dx} = 2x\), so at \(x = 20\) the slope of the tangent is \(f'(20) = 2 \cdot 20 = 40\).
