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| Preface | |
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| Acknowledgements | |
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| Introduction to mathematical modelling | |
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| Mathematical models | |
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| An overview of the book | |
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| Some modelling approaches | |
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| Modelling for decision-making | |
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| Compartmental models | |
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| Introduction | |
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| Exponential decay and radioactivity | |
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| Case Study: Detecting art forgeries | |
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| Case Study: Pacific rats colonise New Zealand | |
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| Lake pollution models | |
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| Case Study: Lake Burley Griffin | |
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| Drug assimilation into the blood | |
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| Case Study: Dull, dizzy or dead? | |
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| Cascades of compartments | |
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| First-order linear DEs | |
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| Equilibrium points and stability | |
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| Case Study: Money, money, money makes the world go around | |
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| Exercises for Chapter 2 | |
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| Models of single populations | |
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| Exponential growth | |
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| Density dependent growth | |
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| Limited growth with harvesting | |
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| Case Study: Anchovy wipe-out | |
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| Case Study: How can 2 x 10[superscript 6] birds mean rare? | |
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| Discrete population growth and chaos | |
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| Time-delayed regulation | |
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| Case Study: Australian blowflies | |
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| Exercises for Chapter 3 | |
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| Numerical solution of differential equations | |
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| Introduction | |
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| Basic numerical schemes | |
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| Computer implementation using Maple and MATLAB | |
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| Instability | |
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| Discussion | |
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| Exercises for Chapter 4 | |
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| Interacting population models | |
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| Introduction | |
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| An epidemic model for influenza | |
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| Predators and prey | |
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| Case Study: Nile Perch catastrophe | |
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| Competing species | |
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| Case Study: Aggressive protection of lerps and nymphs | |
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| Model of a battle | |
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| Case Study: Rise and fall of civilisations | |
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| Exercises for Chapter 5 | |
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| Phase-plane analysis | |
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| Introduction | |
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| Phase-plane analysis of epidemic model | |
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| Analysis of a battle model | |
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| Analysis of a predator-prey model | |
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| Analysis of competing species models | |
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| Closed trajectories for the predator-prey | |
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| Case Study: Bacteria battle in the gut | |
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| Exercises for Chapter 6 | |
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| Linearisation analysis | |
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| Introduction | |
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| Linear theory | |
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| Applications of linear theory | |
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| Nonlinear theory | |
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| Applications of nonlinear theory | |
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| Exercises for Chapter 7 | |
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| Some extended population models | |
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| Introduction | |
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| Case Study: Competition, predation and diversity | |
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| Extended predator-prey model | |
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| Case Study: Lemming mass suicides? | |
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| Case Study: Prickly-pear meets its moth | |
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| Case Study: Geese defy mathematical convention | |
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| Case Study: Possums threaten New Zealand cows | |
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| Exercises for Chapter 8 | |
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| Formulating basic heat models | |
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| Introduction | |
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| Some basic physical laws | |
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| Model for a hot water heater | |
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| Heat conduction and Fourier's law | |
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| Heat conduction through a wall | |
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| Radial heat conduction | |
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| Heat fins | |
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| Exercises for Chapter 9 | |
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| Solving time dependent heat problems | |
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| The cooling coffee problem revisited | |
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| The hot water heater problem revisited | |
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| Case Study: It's hot and stuffy in the attic | |
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| Spontaneous combustion | |
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| Case Study: Fish and chips explode | |
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| Exercises for Chapter 10 | |
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| Solving heat conduction problems | |
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| Boundary value problems | |
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| Heat loss through a wall | |
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| Case Study: Double glazing: What's it worth? | |
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| Insulating a water pipe | |
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| Cooling a computer chip | |
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| Exercises for Chapter 11 | |
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| Introduction to partial differential equations | |
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| The heat conduction equation | |
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| Oscillating soil temperatures | |
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| Case Study: Detecting land mines | |
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| Lake pollution revisited | |
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| Exercises for Chapter 12 | |
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| Differential equations | |
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| Properties of differential equations | |
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| Solution by inspection | |
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| First-order separable equations | |
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| First-order linear equations and integrating factors | |
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| Homogeneous equations | |
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| Inhomogeneous equations | |
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| Further mathematics | |
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| Linear algebra | |
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| Partial derivatives and Taylor expansions | |
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| Review of complex numbers | |
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| Hyperbolic functions | |
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| Integration using partial fractions | |
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| Notes on Maple and MATLAB | |
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| Brief introduction to Maple | |
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| Solving differential equations with Maple | |
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| Brief introduction to MATLAB | |
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| Solving differential equations with MATLAB | |
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| Units and scaling | |
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| Scaling differntial equations | |
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| SI Units | |
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| References | |
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| Index | |