Abstract: In this talk, we will look at calculus through a new lens as we approach the definition of the path-ordered exponential. We will see that the path-ordered exponential arises naturally in the solution of first-order linear systems of ODEs (with variable coefficients) and is also a stepping stone toward path integrals in quantum physics.

99% of this talk will be accessible to undergraduates that have some experience with introductory analysis and linear algebra. However, 1% will be accessible to no one, because it will be utter nonsense.