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# SIMIODE

## OER Materials Modeling Scenario

## 1-115-ModelingWithFirstOrderODEs-ModelingScenario

Author(s): Michael Grayling

University of Cambridge, Cambridge ENGLAND UK

Keywords: bacteria falling object Newton's Law of Cooling drug cooling drag

## Abstract Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.

## Citation

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## Description

The following is material reproduced from a larger mathematics project. All internal references to course work or retained.

The world around us poses many questions that can in theory be better understood using mathematics, and the process of writing down an equation describing how a variable of interest changes according to time or space, is called mathematical modelling.

Unfortunately though, we are usually not able to write down such an equation straight away. But, we can often make simplifying assumptions that allow us to write down its rate of change with time: this gives us a differential equation. Solving this differential equation then gives us the solution to the original problem.

For example; if we wished to describe how the number of bacteria, y, in a particular culture grew with time, t, proceeding to immediately write down a functional form for y's dependence upon t, y(t), is no easy feat. However, if we were to make the assumption that the number of bacteria grows at a rate proportional to its current size we can write down a differential equation for y

## Authors

Author(s): Michael Grayling

University of Cambridge, Cambridge ENGLAND UK