Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students' modelling skills using a combination of case studies and projects.

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Preface Introduction Part I: Ordinary Differential Equations Case Study Al Deterministic Model in Contagious Disease Case Study A2 Electromagnetic Forces in High Field Magnet Coils Project B1 Mass Balance of a Reactor in Steady State Project B2 The Free and Forced Vibration of an Automobile Project B3 Cantilever Beam Subjected to an End Load ODE Problems Part II: Partial Differential Equations Case Study A3 Cylindrical and Spherical Solidification in Heat Transfer Case Study A4 Elastic Analysis of a Square Plate with Circular Holes Project B4 Motion of Fluid Layers Project B5 Mass Balance of a Reactor with Time Dependency Project B6 Flow through Porous Media PDE Problems Part III: Optimization Case Study A5 Linear Programming Problem Involving Wine Production Case Study A6 Transportation Problem Involving Breweries and Hotels Project B7 Profit from an Engineering Plant Project B8 Optimization of Manufacture of Personal Computers Project B9 Air Freight Transportation Problem Optimization Problems Subject Index