1. Interpolation & Numerical Methods

Try these first

1. 1.

   What is the definition of a finite difference?

   Hint

   Think about how one value differs from another.

2. 2.

   Calculate the forward difference Δf(1) when f(1)=1 and f(2)=8.

   Hint

   Use the formula for forward difference.

3. 3.

   What does Δf represent?

   • The change in function value
   • The total value of a function
   • The function itself

   Hint

   It's about the change between two points.

4. 4.

   True or False: The backward difference only uses future value data.

   • True
   • False

   Hint

   Focus on which values are involved.

5. 5.

   Use finite differences to derive the second-order link function from known values at three points: (1, 1), (2, 8), (3, 27).

   Hint

   Think about how differences build upon each other visually.

6. 6.

   Given data points are not equally spaced, explain how you would adapt Newton's backward interpolation formula.

   Hint

   Focus on the key differences in how you find u.