This lecture covers the concept of geodesics as the locally shortest path between points, their appearance in physics, and the principle of least action. It also explains how to define the area of a surface using parametric squares.
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The course provides an introduction to the study of curves and surfaces in Euclidean spaces. We will learn how we can apply ideas from differential and integral calculus and linear algebra in order to
Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.
