Mathematical modelling - Essay Example

In mathematics, modelling offers a means of solving real world problems using mathematics (Berry & Houston, 1995). This is done using the representation of the association between at least two variables that are significant to a given problem. Consequently, mathematical modelling enables people to create or visualize patterns or representations of something to be constructed. This process involves formulating models using real world data obtained from observation, investigation, and evaluation.

Mathematical models are then analysed to establish mathematical conclusions that are interpreted to predict or explain the real world data. The predictions are then tested to establish their applicability, validity, use, and limitations. Mathematical models are used to identify what is real world and conceptual world (Berry & Houston, 1995). In the real world, phenomena and behaviours of natural or artificial systems are observed and using the conceptual world, efforts are made to understand the real world through formulation of a mathematical model, solving resulting equations, and interpreting the results.

With the resulting mathematical models, humans can then offer students the knowledge and skills of creating models and determining the extent to which they imitate the real world. In this report, mathematical models have been used to determine the maximum and minimum heights of two roller coasters. Height is a crucial attribute in the design of actual roller coasters and when determined, it is then related to roller coaster site and the conditions needed to have smooth rides. In this report, the application of mathematical models has involved listing all known variables as a way of identifying the unknown.

This is followed by defining assumptions, and applying the physical principle to be applied to the model. Since to find the maximum height and minimum height the first derivative is zero,