3. Interpolation & Numerical Methods

Try these first

1. 1.

   What is numerical differentiation?

   Hint

   Think about how we deal with tables of values.

2. 2.

   List the three main difference formulas used in numerical differentiation.

   Hint

   These have directions in their names.

3. 3.

   What is numerical differentiation?

   • A method to differentiate analytically
   • Estimating derivatives from discrete data
   • It is obsolete method

   Hint

   Remember how we handle experimental data.

4. 4.

   Round-off error occurs due to:

   • True
   • False

   Hint

   Think about how computers manage decimal values.

5. 5.

   Given a table of values: x | f(x): 0 | 1, 1 | 2, 2 | 0.5, calculate f'(1) using the central difference method and discuss the effect of spacing.

   Hint

   Think about how the choice of spacing affects your calculations.

6. 6.

   Explore the implications of using noisy data for numerical differentiation and propose strategies to mitigate errors.

   Hint

   Consider filtering approaches that are common in data analysis.