Mathematical Modelling with Case Studies: Using Maple and MATLAB, Third Edition, 3rd Edition (Hardback) book cover

Mathematical Modelling with Case Studies

Using Maple and MATLAB, Third Edition, 3rd Edition

By B. Barnes, G..R. Fulford

Chapman and Hall/CRC

388 pages | 143 B/W Illus.

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Mathematical Modelling with Case Studies: Using Maple™ and MATLAB®, Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting populations, and heating/cooling problems, the mathematical techniques presented can be applied to many other areas.

The text carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model-building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. The authors often examine a model numerically before solving it analytically. They also discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model.

The highly recommended second edition was praised for its lucid writing style and numerous real-world examples. With updated Maple™ and MATLAB® code as well as new case studies and exercises, this third edition continues to give students a clear, practical understanding of the development and interpretation of mathematical models.


Praise for the Second Edition:

"The book is written in a very lucid manner, with numerous case studies and examples thoroughly discussed. The material is very well organized, generously illustrated, and delightfully presented. All chapters, except the first one, conclude with scores of nicely designed exercises that can be used for independent study. The book contains enough material to organize a new well-structured one-semester course or to complement the existing one with additional examples and problems and is highly recommended for either purpose"

Zentralblatt MATH, 1168

"The book can be useful for students of mathematical modeling. They will find many skills for modeling and solving real problems. Useful sheets for Maple and MATLAB are included for numerical solution. The most important feature of the book is that it contains many real-life examples. … The main examples are solved in detail and the others are left for the reader. This is the best treasury of real case problems seen in a single book."

EMS Newsletter, September 2009

Table of Contents

Introduction to Mathematical Modeling

Mathematical models

An overview of the book

Some modeling approaches

Modeling for decision making

Compartmental Models


Exponential decay and radioactivity

Case study: detecting art forgeries

Case study: Pacific rats colonize New Zealand

Lake pollution models

Case study: Lake Burley Griffin

Drug assimilation into the blood

Case study: dull, dizzy, or dead?

Cascades of compartments

First-order linear DEs

Equilibrium points and stability

Case study: money, money, money makes the world go around

Models of Single Populations

Exponential growth

Density-dependent growth

Limited growth with harvesting

Case study: anchovy wipe-out

Case study: how can 2 × 106 birds mean rare?

Discrete population growth and chaos

Time-delayed regulation

Case study: Australian blowflies

Numerical Solution of Differential Equations


Basic numerical schemes

Computer implementation using Maple and MATLAB



Interacting Population Models


An epidemic model for influenza

Predators and prey

Case study: Nile Perch catastrophe

Competing species

Case study: aggressive protection of lerps and nymphs

Model of a battle

Case study: rise and fall of civilizations

Phase-Plane Analysis


Phase-plane analysis of epidemic model

Analysis of a battle model

Analysis of a predator-prey model

Analysis of competing species models

The predator-prey model revisited

Case study: bacteria battle in the gut

Linearization Analysis


Linear theory

Applications of linear theory

Nonlinear theory

Applications of nonlinear theory

Some Extended Population Models


Case study: competition, predation, and diversity

Extended predator-prey model

Case study: lemming mass suicides?

Case study: prickly pear meets its moth

Case study: geese defy mathematical convention

Case study: possums threaten New Zealand cows

Formulating Heat and Mass Transport Models


Some basic physical laws

Model for a hot water heater

Heat conduction and Fourier’s law

Heat conduction through a wall

Radial heat conduction

Heat fins


Solving Time-Dependent Heat Problems

The cooling coffee problem revisited

The water heater problem revisited

Case study: it’s hot and stuffy in the attic

Spontaneous combustion

Case study: fish and chips explode

Solving Heat Conduction and Diffusion Problems

Boundary condition problems

Heat loss through a wall

Case study: double glazing: what’s it worth?

Insulating a water pipe

Cooling a computer chip

Case Study: Tumor growth

Introduction to Partial Differential Equations

The heat conduction equation

Oscillating soil temperatures

Case study: detecting land mines

Lake pollution revisited

Appendix A: Differential Equations

Appendix B: Further Mathematics

Appendix C: Notes on Maple and MATLAB

Appendix D: Units and Scaling

Appendix E: Parameters

Appendix F: Answers and Hints



Exercises appear at the end of each chapter.

About the Authors

B. Barnes is a director in the Australian Government Research Bureau and a visiting fellow at the National Centre for Epidemiology and Population Health at the Australian National University, Canberra. She has published work in a number of applied areas, such as bifurcation theory, population dynamics, carbon sequestration, biological processes, and disease transmission.

G.R. Fulford was recently a research associate and senior lecturer in applicable mathematics at the Queensland University of Technology. He has published several textbooks on mathematical modeling and industrial mathematics as well as other work in areas, such as mucus transport, spermatozoa propulsion, infectious disease modeling, tuberculosis in possums, tear-flow dynamics in the eye, and population genetics.

About the Series

Textbooks in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations