Chapter 02.01. Prior Knowledge For Numerical Differentiation.

In this video, we discuss numerical differentiation of continuous functions and the foundational concepts needed to understand it. We start by explaining the concept of a secant line and how it approximates the derivative of a function at a point. As the distance between two points on the function decreases, the secant line becomes a tangent line, representing the exact derivative.

We demonstrate this with an example where the function is f(x) = 7x^2. We calculate the derivative f'(x) = 14x and find the derivative at x = 3, resulting in f'(3) = 42. We also illustrate the numerical approach using the secant line with a finite difference Delta x = 0.5, showing that the approximate derivative closely matches the exact value. This segment reinforces understanding of both analytical and numerical differentiation methods.

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