3.1. Fundamentals of Numerical Differentiation

Try these first

1. 1.

   What is numerical differentiation?

   Hint

   Focus on what it does with data points.

2. 2.

   Name the three primary difference methods.

   Hint

   Look for directional differences.

3. 3.

   What does numerical differentiation estimate?

   • Areas under curves
   • Derivatives of functions
   • Roots of equations

   Hint

   Think about what derivative represents.

4. 4.

   True or False: The Central Difference method uses values on both sides of the target point.

   • True
   • False

   Hint

   Reflect on how averages work.

5. 5.

   Given a set of data points, (x: 0, f(x): 1), (x: 0.5, f(x): 2), (x: 1, f(x): 3), estimate the derivative at x=0.5 using all three difference methods.

   Hint

   Apply each formula carefully to derive results.

6. 6.

   An experimental dataset shows significant noise. What strategies would you implement to reduce numerical differentiation errors?

   Hint

   Think about how errors are influenced by data quality.