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3 cards from this section. Quick, good the night before a test.
What is the initial condition provided in the example?
Think about what value the function starts at.
Calculate y1 using Euler's method with h = 0.1.
Use the formula y1 = y0 + h * f(t0, y0).
What is the formula for updating the solution in Euler's method?
Remember the format used for y in relation to previous values.
Euler's method is classified as which order of method?
Consider how the error decreases with smaller step sizes.
Using Euler's method with h = 0.2, calculate the first three approximations for the equation dy/dt = y, with the initial condition y(0) = 2.
Follow the same iterative update process as in previous examples.
Evaluate the potential error range when using h = 0.5 versus h = 0.1 for the equation dy/dt = 2y, and discuss the implications of larger step sizes.
Analyze how approximations change based on empirical evaluations.
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