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

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.