3rd Edition

Mathematical Modelling with Case Studies Using Maple and MATLAB, Third Edition

By B. Barnes, G..R. Fulford Copyright 2015
    390 Pages 143 B/W Illustrations
    by Chapman & Hall

    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.

    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.


    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.

    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