Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple and MATLAB, Second Edition - Rilegato

Barnes, B.; Fulford, G..R.

Rilegato

ISBN 10: 1420083481 ISBN 13: 9781420083484

Casa editrice: Chapman and Hall/CRC, 2008

Riassunto

Focusing on growth and decay processes, interacting populations, and heating/cooling problems, Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple™ and MATLAB®, Second Edition presents mathematical techniques applicable to models involving differential equations that describe rates of change. Although the authors concentrate on models involving differential equations, the ideas used can be applied to many other areas.

The book 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. They discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model.

Through applications and the tools of Maple™ and MATLAB®, this textbook provides hands-on model building skills. It develops, extends, and improves simple models as well as interprets the results.

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Recensione

"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

Contenuti

Introduction to Mathematical Modeling

Mathematical models

An overview of the book

Some modeling approaches

Modeling for decision making

Compartmental Models

Introduction

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

Introduction

Basic numerical schemes

Computer implementation using Maple and MATLAB

Instability

Discussion

Interacting Population Models

Introduction

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

Introduction

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

Introduction

Linear theory

Applications of linear theory

Nonlinear theory

Applications of nonlinear theory

Some Extended Population Models

Introduction

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 Basic Heat Models

Introduction

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 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

Introduction to Partial Differential Equations

The heat conduction equation

Oscillating soil temperatures

Case study: detecting land mines

Lake pollution revisited

Appendix A: Differential Equations

Properties of differential equations

Solution by inspection

First-order separable equations

First-order linear equations

Homogeneous equations

Inhomogeneous equations

Appendix B: Further Mathematics

Linear algebra

Partial derivatives and Taylor expansions

Review of complex numbers

Hyperbolic functions

Integration using partial fractions

Appendix C: Notes on Maple and MATLAB

Brief introduction to Maple

Using Maple to solve DEs

Brief introduction to MATLAB

Appendix D: Units and Scaling

Scaling differential equations

SI Units

References

Index

Exercises appear at the end of each chapter.

Dettagli dell?edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 1420083481
• ISBN 13: 9781420083484
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 366
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile