Numerical Derivatives of Order 1: Finite Differences Progressive

This lecture introduces the concept of numerical derivatives of order 1 using progressive finite difference formulas. The instructor explains the calculation of derivatives based on differences between function values at different points. The lecture covers the application of these formulas in numerical analysis, specifically focusing on the development of Taylor series. Various examples are provided to illustrate the computation of derivatives and the importance of understanding the relationship between function values. Additionally, the lecture discusses the implications of different choices of parameters on the accuracy of derivative calculations.