Vocabulary
What is Euler’s Method?
This formula approximates solutions to differential equations using tangent line slopes.
dy/dx = x + y, y(0) = 1, h = 0.1, Find y(0.1).
What is 1.1?
dy/dx = x + 2y, y(0) = 1, h = 0.5, Find y(1).
What is 3.125?
If dy/dx > 0 at a point, the function is doing this.
What is increasing?
How do you pronounce Euler?
What is dy/dx?
In Euler’s Method, this value represents the slope at a point.
dy/dx = 2x - y, y(1) = 3, h = 0.5, Find y(1.5).
What is 2.5?
dy/dx = 4 − y, y(0) = 0, h = 0.5, Find y(1).
What is 3?
If dy/dx < 0 at a point, the function is doing this.
What is decreasing?
What century was Euler's Method created?
What is the 18th Century?
What is h?
This symbol usually represents the step size in Euler’s Method.
dy/dx = x - y, y(0) = 2, h = 1, Find y(2).
What is 1?
dy/dx = x^2 − y, y(0) = 2, h = 1, Find y(2).
What is 1?
If dy/dx = 0 at a point, the tangent line is this.
What is horizontal?
Who invented Euler's Method?
Who is Leonhard Euler?
What is a tangent line?
Euler’s Method uses this type of line to approximate curves.
dy/dx = 3x - 2y, y(1) = 2, h = 0.2, Find y(1.2).
What is 1.8?
dy/dx = 3x + y, y(1) = 2, h = 0.5, Find y(2).
What is 9.125?
In Euler’s Method, a larger step size (h) usually makes the approximation this.
What is less accurate?
What is Euler's Constant?
What is e?
What is the step size?
Euler’s Method becomes more accurate when this gets smaller.
dy/dx = y - x^2, y(0) = 1, h = 0.5, Find y(1).
What is 2.125?
dy/dx = y + x, y(0) = 1, h = 0.25, Find y(1).
What is 3.22?
Euler’s Method error builds up because each step depends on this previous value.
What is the previous approximation?
Where was Euler born?
What is Switzerland?