3.5 - Comparison of Methods
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Practice Questions
Test your understanding with targeted questions
What is a finite difference method used for?
💡 Hint: Think about what we do when we can't derive a function analytically.
Name an advantage of the trapezoidal rule.
💡 Hint: Consider the nature of the shape it uses for estimation.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary use of finite difference methods?
💡 Hint: Think about what finite differences are meant to calculate.
True or False: Simpson's rule has a convergence rate of O(h^2).
💡 Hint: Consider the differences in convergence rates we discussed.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Calculate the derivative of f(x) = sin(x) using the central difference method at x = π/4 with h = 0.01.
💡 Hint: Remember the value of sin(π/4) and how to calculate using your methods.
Set up an example using Simpson’s rule to approximate the integral of f(x) = x² from 0 to 2 with 4 intervals.
💡 Hint: What is the structure of Simpson's rule for multiple intervals?
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