From 684546553112cc111514d179835c61b9d2177520 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Zekeriya=20ALTA=C3=87?=
 <153484393+zaltac@users.noreply.github.com>
Date: Tue, 7 Jan 2025 22:13:43 +0300
Subject: [PATCH] Update videos.md

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 [Video 1. Numerical Differentiation Basics](https://www.youtube.com/watch?v=J1E7Wo-Bn-0) In this video, the numerical differentiation and its geometric interpretation are presented. The necessity for numerical differentiation, truncation, and round-off errors is explained. First-order forward and backward, along with the second-order central difference, formulas are derived.
 
 [Video 2. Examples of Numerical Differentiation](https://www.youtube.com/watch?v=GM2jNF5M8nA) In this video, two examples are presented. The first one involves differentiating an explicitly known function illustrating the effect of reducing h on forward and central difference formulas. The second example involves a discrete dataset for which first and second derivatives are estimated using second-order difference formulas.
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+[Video 3. Finite Differences and Direct-Fit Polynomialsn](https://www.youtube.com/watch?v=DPMLPhcGv1s) This video covers deriving  finite difference (forward, backward, central) equations using direct-fit polynomials using uniformly and nonuniformly distributed data points.
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+[Video 4. Numerical Differentiation via Richardson Extrapolation](https://www.youtube.com/watch?v=kaseVNv-7KM) This video describes the application of Richardson extrapolation to numerical differentiation. The construction of Richardson table is illustrated for the first derivative using central difference formula. A numerical example with step-by-step explanations is also given for a better understanding of the theory.