# Features

Developed primarily for non-specialists studying mathematics as part of a degree course needing to build up their mathematical skills, these two online packages introduce topics using illustrative media which has been designed to ease students into the theory as well as demonstrating how mathematical concepts relate to straightforward, everyday ideas.

This unique approach quickly brings students of varying ability up to speed in addition to taking the anxiety out of studying mathematics!

## Key Course Features include:

A fully integrated suite of learning tools designed to boost student engagement and provide a contextual background for the key concepts.

Material is broken down into modules consisting of bite-sized chunks of content, with all media and assessment linked directly to learning objectives.

Each module begins with clear and concise learning objectives, self-assessment questions and hyperlinked pre-requisites so students can quickly navigate back to topics that might require further study.

Extension material allows students to explore beyond the core content.

Each module features interactive tools so that the student can practice and play with concepts for comprehension.

#### An extensive range of embedded media helps boost student engagement and contextualise key concepts...

## Applets

These allow students to interact directly with the theory by playing with the data and observing the results on screen.

## Mathematics in Context

These videos provide real-life context to the theory and allow students to test their understanding.

In the problem where a ball falls from 5m under gravity (g=10), with no air resistance, the time it takes for the ball to reach the floor is found by solving

5t^{2}=5

so that t=1. So we expect an answer near to 1. Now let's look at the example with the small amount of air resistance.

One method for solving the equations is rearranging the equation so that the original equation:

5=100t-1000(1-e^{-0.1t})

becomes:

t=0.5+10(1-exp(-0.1t))

and then we iterate

n | tm |
---|---|

0 | 1 |

1 | 1.0016 |

2 | 1.0031 |

3 | 1.0044 |

5 | 1.0067 |

10 | 1.0108 |

20 | 1.0147 |

40 | 1.0167 |

80 | 1.0169 |

160 | 1.0169 |

Solution to 4dp is 1.0169

**Consider the equation x ^{2} – x = 0. Which of these is the iteration equation to solve this equation.**

- x=x
^{2}* - x=sin(x)
- x
^{2}=x - y=mx+c

**For the previous question what will happen if you start the iteration with x _{0}=0.5?**

- Iterates converges to 1
- Iterates converge to 0*
- Iterates do not converge

**What happens if you start the iteration with x _{0}=1.5?**

- Iterates converges to 1
- Iterates converge to 0
- Iterates do not converge*

## Animations

Produced by the author team these animations guide students through tricky concepts and are accompanied by easy-to-follow narration.