AP Calculus BC glossary
Euler's method
Euler's method approximates the solution of a differential equation by starting at a known point and repeatedly stepping along the tangent line for a small increment. Each step uses the differential equation to compute the slope at the current point.
It is linearization applied over and over. Each step is exactly a tangent line approximation, and the new endpoint becomes the starting point for the next one.
The error direction follows concavity: if the true solution is concave up, the tangent lines lie below it and Euler's method underestimates. Smaller steps reduce the error but never eliminate it.
The mistake
Reusing the initial slope for every step. The slope must be recomputed at each new point, which is the entire reason the method works.
Appears in: Unit 7: Differential Equations