The Kronig-Penney problem is a textbook example for discussing band dispersions and band gap formation in periodic layered media. For example, in photonic crystals, the behaviour of bands next to the band edges is important for further discussions of such effects as inhibited light emission, slow light and negative index of refraction. However,…

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

Presents a class activity in which students use trigonometry to calculate the height attained by a water rocket. Provides a lesson plan that includes a list of materials needed, procedures to carry out the experiment, suggestions to extend the activity, and a reproducible worksheet for the students to register their calculations. (MDH)