## Topic 6 - Calculus (40 hours)

The aim of this topic is to introduce students to the basic concepts and techniques of differential and integral calculus and their applications.

## Calculus - What You Should Know

The document "what_you_should_know_-_calculus" below is where you will find key descriptions of the content of of Calculus. The document outlines the mathematical concepts that make up the content of the topic. Some examples are provided that illustrate how these concepts have been presented in past exams, along with some commentary towards a solution to the example. There is also some "Be prepared" comments that focus your attention on common issues to help you prepare more thoroughly.

calculus_what_you_should_know.pdf | |

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calculus_revision_guide.pdf | |

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**What Calculus Does for U****s.**

*Source: I. Stewart "Taming the Infinite." Quercus, 2008*

**: they are by far the commonest way to model natural systems. To choose one application at random, they are used routinely to calculate the trajectories of space probes, such as the Mariner mission to Mars, the two Pioneer craft that explored the solar system and gave us such wonderful images of Jupiter, Saturn, Uranus and Neptune, and recently NASA's Mars Curiosity.**

*Differential equations abound in science*The Cassini mission, currently exploring Saturn and its moons, is another example. Among its discoveries is the existence of lakes of liquid methane and ethane on Saturn's moon Titan. Of course, calculus is not the only technique used by space missions--but without it, these missions would literally never have got off the ground.

More practically, every aircraft that flies, every car that travels the road and every suspension bridge and earthquake-proof building owes its design in part to calculus. Even our understanding of how animal populations change size over time stems from differential equations. The same goes for the spread of epidemics, where calculus models are used to plan the most effective way to intervene and prevent disease spreading. A recent model of the foot and mouth disease epidemic in the UK has shown that the strategy adopted at the time was not the best available.