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3 cards from this section. Quick, good the night before a test.
What is the error characteristic of the forward difference method?
Think about how the error changes with the step size.
What do you call the distance between discrete data points in finite difference methods?
This term is used to denote the incremental change.
What is the error rate for forward and backward difference methods?
Remember the relationship between error and the method used.
True or False: Central differences have a quadratic error reduction as step size decreases.
Think about how the method affects accuracy.
Given the function f(x) = sin(x), calculate the derivative using both forward difference and central difference methods at x = π/4 with h = 0.01. Compare the two errors with respect to the actual derivative cos(π/4).
Document step calculations for both methods to observe the differences in error explicitly.
Discuss a scenario in engineering where approximating a derivative with a large step size might be acceptable despite potential errors. Justify your answer based on computational cost versus accuracy.
Think about contexts in engineering where time is a constraint, but perfect precision is not critical.
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