The transcendental elementary functions are traditionally introduced in the high school/(pre)calculus courses in the way that obscures their inter-relations and properties. The text below is an extended version of the one-hour lecture delivered on Ulpana de-Shalit for undergraduate students. It purports to introduce these functions as solutions to linear differential equations in the way similar to radicals being introduced as solutions to algebraic equations.

Polynomials, matrices and differential equations, 11 pages (pdf).