1.1.3. Difference Table

Try these first

1. 1.

   What is a finite difference?

   Hint

   Think about how we approximate derivatives.

2. 2.

   How is the first row of a difference table set up?

   Hint

   Recall the function values are organized as x₀, x₁, and their corresponding f values.

3. 3.

   What is the primary function of a difference table?

   • To approximate integrals
   • To compute finite differences
   • To solve differential equations

   Hint

   Recall its use in interpolation.

4. 4.

   True or False: The second row of a difference table contains actual function values.

   • True
   • False

   Hint

   Think about what each row is meant to convey.

5. 5.

   Given values of a function at specific points create a complete difference table and derive an interpolation formula.

   Hint

   Pay attention to how differences build on each other.

6. 6.

   Explain how to use a difference table to predict unmeasured function values.

   Hint

   Think about the pattern of differences and how they guide approximation.