3. Numerical Differentiation
Numerical differentiation is a vital method for estimating derivatives of functions based on discrete data points, particularly when analytical solutions are not available. Various finite difference formulas—forward, backward, and central differences—are employed, depending on the positioning of the point of interest within the data. While highly effective, numerical differentiation requires careful application to mitigate errors arising from truncation and round-off.
Enroll to start learning
You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- Numerical differentiation estimates the derivative of a function at discrete points.
- Different formulas (forward, backward, central) are used based on data characteristics.
- Careful selection of formulas and step sizes is essential due to potential errors.
Key Concepts
- -- Numerical Differentiation
- A method of estimating the derivatives of functions when only discrete data is available.
- -- Forward Difference
- A method for approximating derivatives using values at points ahead of the point of interest.
- -- Backward Difference
- A method for approximating derivatives using values at points behind the point of interest.
- -- Central Difference
- A method for approximating derivatives using values on both sides of the point of interest.
- -- Error in Numerical Differentiation
- Numerical differentiation errors arise from truncation and round-off, requiring careful analysis.
Additional Learning Materials
Supplementary resources to enhance your learning experience.