4 - Interpolation & Numerical Methods
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Practice Questions
Test your understanding with targeted questions
Explain the Trapezoidal Rule in your own words.
💡 Hint: Think about how you would use rectangles versus trapezoids.
What do you need to ensure for Simpson’s Rule to work?
💡 Hint: Consider the formula that defines Simpson's 1/3 Rule.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main purpose of numerical integration?
💡 Hint: Think about why we would use numerical methods.
True or False: Simpson's 1/3 Rule can be applied to odd numbers of intervals.
💡 Hint: Think about the conditions for the formula.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Using both the Trapezoidal Rule and Simpson's 1/3 Rule, approximate the integral of f(x)=ln(x) from 1 to 2 using four intervals. Compare results.
💡 Hint: Calculate each step carefully and ensure to divide the range correctly.
Create a Python program to implement and compare the results of the Gauss-Kronrod quadrature method with Simpson's 3/8 Rule for a complex function like sin(x).
💡 Hint: Focus on structuring your function correctly and handling intervals effectively.
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