Euler's Method | Brilliant Math & Science Wiki
brilliant.org › wiki › eulers-methodThe idea behind Euler's method is to remedy this by repeatedly using tangent line approximations; so, for example, to approximate f (x + 3 h) f(x+3h) f (x + 3 h) by first approximating f (x + h) f(x+h) f (x + h), then f (x + 2 h) f(x+2h) f (x + 2 h), and then f (x + 3 h) f(x+3h) f (x + 3 h). At each step, we use the slope of the curve to construct the next line segment, and this allows us to "follow" the curve with line segments, as shown in the image to the right.