Practice Flashcards
What is the Euler recurrence for dy/dx = f(x, y)?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 5.16
Below are all 8 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
5.16.18 cards
What is the Euler recurrence for dy/dx = f(x, y)?
y_(n+1) = y_n + h·f(x_n, y_n) and x_(n+1) = x_n + h, starting from (x₀, y₀).
How many Euler steps reach a target x from x₀ with step length h?
number of steps = (target − x₀) ÷ h. E.g. x = 1 to x = 2 with h = 0.25 is 4 steps.
What does each Euler step actually do geometrically?
It moves along a short STRAIGHT line at the gradient measured at the current point — so the path only approximates the true curve.
Is Euler's method exact?
No — it is an approximation. A smaller step length h gives more steps and a more accurate estimate, but never the exact value.
Does Euler over- or under-estimate?
It depends on the curve's concavity: it tends to UNDER-estimate for a concave-up curve and OVER-estimate for a concave-down curve.
Which gradient does each Euler step use?
The gradient f(xₙ, yₙ) at the START of the step (the point you are currently at), not at the new point.
How do you find the percentage error of an Euler estimate?
percentage error = |approx − exact| ÷ exact × 100%, using the exact solution given in the question.
What is the GDC route for Euler's method in AI?
Store the recurrence as a recursive sequence (or fill a table of n, xₙ, yₙ, gradient); a calculator is allowed on every AI paper.
Topic 5.16 study notes
Full notes & explanations for Euler's method (1st order) (HL only)
Math AI exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free