Practice Interpolation & Numerical Methods (1) - Finite Differences - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is the definition of a finite difference?
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Think about how one value differs from another.
Question 2.
Calculate the forward difference Δf(1) when f(1)=1 and f(2)=8.
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Use the formula for forward difference.
3Question 3.
What does Δf represent?
- The change in function value
- The total value of a function
- The function itself
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It's about the change between two points.
4Question 4.
True or False: The backward difference only uses future value data.
- True
- False
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Focus on which values are involved.
Question 5.
Use finite differences to derive the second-order link function from known values at three points: (1, 1), (2, 8), (3, 27).
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Think about how differences build upon each other visually.
Question 6.
Given data points are not equally spaced, explain how you would adapt Newton's backward interpolation formula.
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Focus on the key differences in how you find u.

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