1.1. Finite Differences

Try these first

1. 1.

   What is the formula for the forward difference?

   Hint

   Think about how the function values change with a small increment.

2. 2.

   What is the backward difference at point x?

   Hint

   Consider the value at the current point and the previous point.

3. 3.

   What does the forward difference measure?

   • Decrease in function value
   • Change in function value as x increases
   • Average change

   Hint

   Recall the forward difference formula.

4. 4.

   True or False: The central difference provides less accuracy than the forward and backward differences.

   • True
   • False

   Hint

   Consider the definitions of each type of difference.

5. 5.

   Given the function f(x) = sin(x) at x = 0, π/6, π/3, π/2, find the first forward differences.

   Hint

   Substitute the values of sin function at the mentioned points.

6. 6.

   Derive the central difference formula from the definitions of forward and backward differences.

   Hint

   Consider the symmetrical nature of central differences.