Modelling nature: an introduction to mathematical modelling of natural systems

Abstract

Abstract This book with 6 chapters introduces basic concepts in mathematical modelling applied to natural systems to tackle real-world problems from fields such as physics, ecology, geology and epidemiology. It shows how using models can help to unravel complex issues such as the melting of the Arctic ice, the spread of infectious disease and the age of the Earth. Each chapter of this book focuses on a different problem using real-world data. For each problem, a mathematical model is developed and used to make predictions. To make this process easier, each chapter is further divided into five parts. The first part of each chapter introduces the problem. This includes the motivation of why it might be interesting in the first place, showing some of the data and making any initial guesses for an appropriate mathematical model. In the second part, an initial mathematical model was developed for the problem. Once the initial model was built, it can be observed at the end of the second part that the models tend to have serious failings. These shortcomings is addressed on the third part of the chapter. This might mean a process of more carefully phrasing the assumptions going into the model to identify its failings. Alternatively, it might go much further and develop a highly sophisticated model using advanced mathematical techniques. With the model built, the fourth part contains some conclusions, relating the model constructed for more sophisticated studies and discussing some potential impacts of the results. Finally, the fifth part contains information about resources for further reading, the sources of data used in the chapter, and suggestions for further work. The text will help students to build steadily upon a basic level of mathematics, to a more advanced understanding of mathematical concepts, for a thorough understanding of a variety of mathematical techniques.