Numerical methods as an introduction to calculus

French, and Samuel A.; Cullerne, John P.; Kanchanasakdichai, O.

doi:10.1088/1361-6552/aaefd1

Cited by 2 publications

(4 citation statements)

References 3 publications

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“…To permit our results to be replicated and extended by students, the computational work can be achieved using nothing more than a standard issue calculator and a spreadsheet, though as in previous papers [4,5] we show this project can be more fully explored if a student implements their mathematical recipes in a coding environment such as MATLAB, a programming language that is widely used during undergraduate courses in the UK. To this end we have developed an intuitive software tool that can enable an epidemiological model to be rapidly fitted to field data.…”

Section: Introductionmentioning

confidence: 81%

“…We shall refer to this trio as the Eyam equations in the subsequent discussion. Rather than use the equations as motivation for a student making their initial forays into Calculus, (as we did in 'The Epidemiology of Eyam' [4], and 'Numerical Methods as an Introduction to Calculus' [5]) let us now assume a greater prowess with mathematical technique; i.e. the tools a first year undergraduate in Physics should hopefully be familiar with.…”

Section: The Eyam Equationsmentioning

confidence: 99%

“…If ρ can be found for a given infection, then this represents a threshold for the epidemic. If the 'local susceptible' population 5 is less than this, then the Eyam model predicts the number of infectives will reduce rather than grow. Without any further investigation, it is clear that I(t) must form a single peaked curve, if the initial susceptible population is > ρ.…”

Section: The Ups and Downs Of Imentioning

confidence: 99%

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The pedagogical power of context: extending the Epidemiology of Eyam

Cullerne

French²,

Poon³

et al. 2019

Phys. Educ.

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Since the introduction of the Extended Project Qualification (EPQ) in 2006, the number of students taking up the qualification has increased dramatically. The research aspect of the activity allows students to develop independent study skills, which are beneficial for subsequent work at University, especially if the EPQ involves rigorous academic content developed over an extended period. Our Epidemiology of Eyam project has provided a rich seam of material for extended study, which has so far engaged a great many of the students at Winchester College. We hope that it will continue to engage students at Winchester, and elsewhere, as the study develops. Importantly, this project generates opportunities for interdisciplinary research. There is scope for collaborative work across subjects including the physical and biological sciences, mathematics and economics. Whereas our previous paper [4] set the contextual scene and provided an introduction to calculus and associated numerical techniques, in this article we demonstrate that the elegant work in infectious disease epidemiology from the first half of the twentieth century [1,2,3] can be presented in an accessible way to pre-university students, providing them with a powerful context to delve into interesting problems and incentivising the acquisition of more advanced methods and skills. The techniques we employ to analyse data from the Eyam plague outbreaks of the 1660s can also be used with data from modern day epidemics, as we show in the context of the 2014 Ebola epidemic in West Africa [6,11,12,13]. To permit our results to be replicated and extended by students, the computational work can be achieved using nothing more than a standard issue calculator and a spreadsheet, though as in previous papers [4,5] we show this project can be more fully explored if a student implements their mathematical recipes in a programming environment such as MATLAB. To this end we have developed an intuitive software tool that can enable an epidemiological model to be rapidly fitted to field data. From a time series of Infective population for the 2014 Liberia Ebola epidemic [6] we can predict Infective   It , Susceptible () St and Dead () Dt populations, calculate the associated population N , calculate the Kendall Susceptible threshold  , and hence the Basic Reproduction Number 0 RN   . For the Liberia Ebola data, these are: 0 2542, 1373, 1.85 NR     . Note this suggests that out of an 'at risk' population of 2542 N  , about 75% may ultimately die of Ebola. In the WHO Ebola Response Team report [15], 0 1.83 0.11 R  for the 2014 Liberia outbreak.

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Section: Introductionmentioning

confidence: 81%

Section: The Eyam Equationsmentioning

confidence: 99%

Section: The Ups and Downs Of Imentioning

confidence: 99%

See 1 more Smart Citation

The pedagogical power of context: extending the Epidemiology of Eyam

Cullerne

French²,

Poon³

et al. 2019

Phys. Educ.

View full text Add to dashboard Cite

show abstract

“…[1]), GNU Octave (https://www.gnu.org/software/ octave/), Modellus (see e.g. [21]), Easy Java Simulations package (https://www.um.es/ fem/EjsWiki/, see e. g. [3,14]), iterative solvers Euler and Verlet [5] or employ standard programming languages directly (PHP, variants of C, Java, Fortran, Python, etc. ).…”

Section: Introductionmentioning

confidence: 99%

Geogebra supporting materials for introductory physics university courses

Richterek,

Říha,

Hrouzková

et al. 2024

J. Phys.: Conf. Ser.

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In this contribution, we present a set of Geogebra activities used in several introductory courses on Classical mechanics, Special relativity, Introductory course to cosmology and within the courses for non-physics majors (Physics for chemists, Physics for biologists). Examples include various oscillations, curvilinear coordinates, solutions of equations of motion, basic types of Minkowski spacetime diagrams and the effective potential for the dynamic of basic cosmological models. All the activities include basic interactivity and the possibility to play with selected parameters. They are used within the classrooms and shared with the students via links in the Moodle LMS platform together with other supporting materials.

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Numerical methods as an introduction to calculus

Cited by 2 publications

References 3 publications

The pedagogical power of context: extending the Epidemiology of Eyam

The pedagogical power of context: extending the Epidemiology of Eyam

Geogebra supporting materials for introductory physics university courses

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