Newton Interpolation and Divided Differences

In this video, we introduce the Newton Interpolation method and Divided Differences. We start with the general concept, then the recurrence relation and the divided difference table. Finally, we run through a quick example in order to understand how the method is used in practice.

Chapters
0:00 - Introduction
05:40 - The Recurrence Relation
10:56 - The Divide Difference Table
12:48 - Example

Errata and Clarifications:
- at 9:00, the numerator should read (x_k - x_0)qn(x_k) + (x_n+1 - x_k)pn(x_k)

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In-video References:
1. "Applied Numerical Methods with MatLab" by Steven C. Chapra -https://amzn.to/3quGfE1
2. "Approximation Theory and Methods" by M.J.D. Powell - https://amzn.to/3JazCy6

FAQ : How do you make these animations?
Animations are made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). Editing and voiceover work in DaVinci Resolve.

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