Follow the slope: Euler's method

Step through a cooling drink, a fall with drag or growth, one slope at a time.

Interactive

step Δt6 min

Euler's answer20.7°C

exact23.5°C

error4.2%

Equation

Number of steps5Rate constant k0.1

The math, with your numbers

\frac{dT}{dt} = -0.1\,(T - 20)

y_{\text{next}} = y + \text{slope} \times \Delta t =90 + (-7) \times 6 = 48

The second line is the first step. Each step after it does the same from where the last one landed.

Try this

→Cooling: with only a few steps, Euler cools the drink too fast. How many steps until the error is under 1%?
→Fall with drag: what speed does every path level off at? Change k and compare with 9.8 / k.
→Growth: does Euler come out too high or too low? Why, looking at how the slope changes?

Want to know why it behaves like this?

The lesson “Differential Equations: Laws of Change” explains it step by step: If physics only tells you how fast things change, how do you find where they end up?

Read the lesson

Follow the slope: Euler's method

Step through a cooling drink, a fall with drag or growth, one slope at a time.

Follow the slope: Euler's method

Interactive

step Δt6 min

Euler's answer20.7°C

exact23.5°C

error4.2%

Equation

Number of steps5Rate constant k0.1

The math, with your numbers

\frac{dT}{dt} = -0.1\,(T - 20)

y_{\text{next}} = y + \text{slope} \times \Delta t =90 + (-7) \times 6 = 48

The second line is the first step. Each step after it does the same from where the last one landed.

Try this

→Cooling: with only a few steps, Euler cools the drink too fast. How many steps until the error is under 1%?
→Fall with drag: what speed does every path level off at? Change k and compare with 9.8 / k.
→Growth: does Euler come out too high or too low? Why, looking at how the slope changes?

Want to know why it behaves like this?

The lesson “Differential Equations: Laws of Change” explains it step by step: If physics only tells you how fast things change, how do you find where they end up?

Read the lesson