Vibrating String: Mathematical Analysis

This lecture introduces the study of a vibrating string as a fundamental example to understand wave equations. The derivation of the 1D wave equation for both infinite and finite systems is covered, along with the concept of transverse displacement. The lecture explores the evolution equation, sinusoidal waves in infinite and finite systems, and the discretization of the wave equation. It also delves into the eigenvalue problem related to the differential operator, emphasizing the importance of boundary conditions and the orthogonality of eigenvectors.