Normal Curvature

This lecture covers the concept of normal curvature on a surface, focusing on the normal section and the oriented curvature. It explains how the surface curvature depends on the direction of the normal section and how to calculate the normal curvature. The lecture also delves into the existence of the normal curvature and provides a detailed proof of the directed curvature. Through the use of an orthonormal basis, the lecture demonstrates the oriented curvature of a surface and how to apply the curvature formula. The content progresses to discuss the elimination method for finding the curvature and the complexities involved in the calculations.