Practice Finite Differences (2.2) - Interpolation Formulas - Mathematics - iii (Differential Calculus) - Vol 4

Practice: Finite Differences

Lesson 2.2Interpolation Formulas

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8 questions

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6 sample questions

Question 1.
Calculate the forward difference for the points (3, 6) and (4, 10).
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Remember the forward difference formula Δy = y(i+1) - y(i).
Question 2.
What is the backward difference for the points (5, 15) and (4, 10)?
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Use the backward difference formula ∇y = y(i) - y(i-1).
3Question 3.
What is the formula for the forward difference?
- Δy = y(i+1) - y(i)
- ∇y = y(i) - y(i-1)
- Central = (Δy + ∇y)/2
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Look for the option using next point.
4Question 4.
True or False: Backward difference calculates the change between a point and the following point.
- True
- False
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Recall the definition of backward difference.
Question 5.
Given the data points (1, 3), (2, 5), (3, 7), and (4, 11), calculate and interpret both forward and backward differences.
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Use the differences as you progress through the data points.
Question 6.
How would a change in the central point affect the interpolation of the surrounding points? Provide a mathematical example.
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Consider realigning data points to see the effects.

4 more questions in this section. Enroll free to practise them all.