3.3. Newton’s Backward Difference Formula for Derivatives

Try these first

1. 1.

   What is the basic formula for the first derivative at the end of the data set using backward difference?

   Hint

   Think about how we represent the operation of difference.

2. 2.

   Define round-off error in the context of numerical methods.

   Hint

   It involves how calculations can deviate due to limited digits.

3. 3.

   What does the backward difference formula estimate?

   • Integrals
   • First and second derivatives
   • Functions

   Hint

   Remember what numerical differentiation is used for.

4. 4.

   True or False: Backward difference uses earlier data points in calculations.

   • True
   • False

   Hint

   Think about which end of the dataset it targets.

5. 5.

   Given a table of values for a function at points (2, 0.9), (2.2, 1.7), (2.4, 2.5), calculate the first derivative at the last point (2.4) using backward difference.

   Hint

   Fill in the required y-values from your table.

6. 6.

   In a physics experiment, the acceleration of an object at different time intervals is recorded. Apply backward difference to find the changes in acceleration at the last recorded time.

   Hint

   Set up your calculations step-by-step with the values.