📘 Chapter 1: Polynomial Interpolation and Approximation

In this chapter, you will learn how to construct polynomials that approximate or reconstruct a function from a set of discrete points. These methods are widely used in signal processing, data compression, and digital transmission to interpolate missing or noisy data.

• 🔹 Explain the fundamental concepts of polynomial interpolation and approximation.
• 🔹 Apply different interpolation methods, including Lagrange, Newton, and Hermite.
• 🔹 Construct polynomial approximations from experimental or simulated data.
• 🔹 Use the least-squares method to fit functions when data cannot be perfectly interpolated.
• 🔹 Analyze interpolation errors to assess the quality of the approximations.