2. Numerical Methods

Numerical Differentiation — Quiz

Test your understanding of numerical differentiation with 5 practice questions.

Practice Questions

Question 1

Which differentiation technique approximates derivatives by representing the function at Chebyshev collocation points and applying a global differentiation matrix to achieve spectral accuracy?

Question 2

Which noise‐robust differentiation method fits a local polynomial in a sliding window to smooth data and compute derivatives simultaneously?

Question 3

Which regularization approach to numerical differentiation treats differentiation as an ill‐posed inverse problem and stabilizes the solution by truncating small singular values?

Question 4

If the step size $h$ in the centered‐difference approximation $f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}$ is halved, by what factor does the leading‐order truncation error change?

Question 5

Using the first‐order forward‐difference formula $f'(x)\approx\frac{f(x+h)-f(x)}{h}$ with $h=0.01$, approximate $f'(1)$ for $f(x)=\ln(x)$.