Mathematical Modelling With Case Studies

Mathematical Modelling with Case Studies provides students with a firm grounding in basic modelling skills applicable to a wide variety of problems. The focus is on models involving differential equations, with the solution of differential equations as the primary technique used.The models considered relate to growth and decay processes, interacting populations, and heating/cooling problems, but the range of applications and mathematical techniques presented provide a broad appreciation of the scope of this type of modelling, while the skills developed readily transfer to many other areas. Within each modelling section of the book, the authors carefully consider the procedure for constructing a model, emphasizing a start simple, evaluate, and then extend process. They use flow diagrams and word equations and discuss the assumptions made, consequent limitations, and impact on the interpretation of results--a structured, detailed approach that has proved a successful learning strategy. Along with theoretical and computational tools for analysis, the authors also encourage graphical methods and integrate throughout the text MAPLE code and its ensuing results. The prerequisites for this text are minimal, including only a basic knowledge of calculus and fundamental computing skills. Thus the book is an excellent choice both for mathematics students and for those in the many other fields of study that require some expertise in modelling.