The Laplace approximation to integrals! This scores well on all points: it is elementary (could be taught in calculus 1) and very useful. Within 30 minutes there should be time to some application, dependent on the audience, maybe the Stirling approximation to the factorial (which is often useds without any proof).

The Laplace approximation to integrals! This scores well on all points: it is elementary (could be taught in calculus 1) and very useful. Within 30 minutes there should be time to some application, dependent on the audience, maybe the Stirling approximation to the factorial (which is often used without any proof).

The Laplace approximation to integrals! This scores well on all points: it is elementary (could be taught in calculus 1) and very useful. Within 30 minutes there should be time to some applicaction, dependent on the audience, maybe the Stirling approximation to the factorial (which is often useds without any proof).

The Laplace approximation to integrals! This scores well on all points: it is elementary (could be taught in calculus 1) and very useful. Within 30 minutes there should be time to some application, dependent on the audience, maybe the Stirling approximation to the factorial (which is often useds without any proof).