2.2. Finite Differences

Try these first

1. 1.

   Calculate the forward difference for the points (3, 6) and (4, 10).

   Hint

   Remember the forward difference formula Δy = y(i+1) - y(i).

2. 2.

   What is the backward difference for the points (5, 15) and (4, 10)?

   Hint

   Use the backward difference formula ∇y = y(i) - y(i-1).

3. 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

   Hint

   Look for the option using next point.

4. 4.

   True or False: Backward difference calculates the change between a point and the following point.

   • True
   • False

   Hint

   Recall the definition of backward difference.

5. 5.

   Given the data points (1, 3), (2, 5), (3, 7), and (4, 11), calculate and interpret both forward and backward differences.

   Hint

   Use the differences as you progress through the data points.

6. 6.

   How would a change in the central point affect the interpolation of the surrounding points? Provide a mathematical example.

   Hint

   Consider realigning data points to see the effects.