Mathematical Modelling (Supporting Early Learning)

Mathematical modelling modules feature in most university undergraduate mathematics courses. As one of the fastest growing areas of the curriculum it represents the current trend in teaching the more complex areas of mathematics. This book introduces mathematical modelling to the new style of undergraduate - those with less prior knowledge, who require more emphasis on application of techniques in the following sections: What is mathematical modelling?; Seeing modelling at work through population growth; Seeing modelling at work through published papers; Modelling in mechanics. Written in the lively interactive style of the Modular Mathematics Series, this text will encourage the reader to take part in the modelling process. Front Cover 1 Mathematical Modelling 4 Copyright Page 5 Table of Contents 6 Series Preface 8 Preface 10 Chapter 1. What is Mathematical Modelling? 12 1.1 Modelling with Data 12 1.2 Using Mathematical Models 21 1.3 Modelling from Theory 23 Chapter 2. Modelling Population Growth. 36 2.1 Understanding the Problem 36 2.2 Choosing Variables. 42 2.3 Making Assumptions 44 2.4 Solving the Equations 45 2.5 Interpreting the Solutionand Validating the Model 46 2.6 Criticising and Improving the Model. 46 Chapter 3. Mathematical Modelling in Action 54 3.1 Introduction 54 3.2 Howto use the Articles. 54 Chapter 4. Developing Modelling Skills. 111 4.1 Modelling Problems 111 4.2 Simulation Modelling 116 4.3 Dimensional AnalysisModelling 128 Answers to Selected Problems 139 Index of Modelling Problems 154 Index 156 Assuming virtually no prior knowledge, Modular Mathematics encourages the reader to develop and solve real models, as well as looking at traditional examples. Accessible and concise, it contains tutorial problems, case studies and exercises One of the simplest mathematical models is a linear one which represents the relation between two variables by a straight line graph.