We derive conservation laws from symmetry operations using the principle of least action. These derivations, which are examples of Noether's theorem, require only elementary calculus and are suitable for introductory physics. We extend these arguments to the transformation of coordinates due to uniform motion to show that a symmetry argument applies more elegantly to the Lorentz transformation than to the Galilean transformation.

We present a method for introducing students to the classical principle of least action, using a novel approach based on the ordinary calculus of one variable. We define the classical action for a path and draw the connection between it and Newton's laws for a free particle and for a particle in a conservative potential. The use of software to help students visualize the principle of least action and analyze rectilinear motion is discussed. We also briefly discuss the origin of the principle of least action in Feynman's sum over paths formulation of quantum mechanics.