When students of the physical sciences transition from school to university, they discover that knowledge of calculus is as vital as arithmetic, and that there is precious little useful information written without calculus. However, the lack of calculus in pre-university physics studies persists, especially in its application to the modelling of physical systems. Introductory courses at university in calculus often have a very different style to school-level work, and consequently many students find the step up difficult. This paper hopes to convey some examples of school-level work in numerical methods that can provide useful visualisations to aid comprehension and to incentivise the acquisition of skills in calculus. The modern pre-university student of the physical sciences would also do well to develop the precursors to coding, and learn the basics of modelling using spreadsheets.

This paper develops the ideas of The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam (French et al 2018 J. Phys. Educ.), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work in numerical methods that can provide useful visualisations to aid in comprehension and to incentivise the acquisition of skills in calculus. We recommend that the modern preuniversity student of the physical sciences would do well to develop the precursors to coding, and learn the basics of modelling using spreadsheets in tandem with analytical methods that dominate contemporary schemes of work. In the present paper, we consider how the firstorder Euler (Press et al 2003 Numerical Recipes in C++: the Art of Scientific Computing 2nd edn (Cambridge: Cambridge University Press) pp 712-55) iterative method may be extended to provide a useful platform to embark on introductory work in more accurate Verlet (https:// en.wikipedia.org/wiki/Verlet_integration (Accessed: 2 September 2018)) techniques, particularly with applications to the solution of second order ordinary differential equations.