Skip to content

Mathematical Modelling with Case Studies A Differential Equations Approach Using Maple and MATLAB

Best in textbook rentals since 2012!

ISBN-10: 1420083481

ISBN-13: 9781420083484

Edition: 2nd 2008 (Revised)

Authors: Belinda Barnes, Glenn Robert Fulford, Glenn Fulford

List price: $91.95
Blue ribbon 30 day, 100% satisfaction guarantee!
what's this?
Rush Rewards U
Members Receive:
Carrot Coin icon
XP icon
You have reached 400 XP and carrot coins. That is the daily max!


For students of applied mathematics, this textbook provides an introduction to the modeling process and its numerous applications at an elementary level. For students from other disciplines, it presents the mathematical basis to encourage a better understanding and analysis of the models they may use. All students gain confidence with a range of analytical tools, including Maple and MATLAB . Introductions to these software programs can be found in the appendices and the codes are available for download online. The book covers a wide range of topics, from environmental science to archaeology. In each section, it includes case studies based on research papers.
Customers also bought

Book details

List price: $91.95
Edition: 2nd
Copyright year: 2008
Publisher: CRC Press LLC
Publication date: 12/18/2008
Binding: Hardcover
Pages: 368
Size: 7.32" wide x 10.35" long x 0.94" tall
Weight: 2.002
Language: English

Introduction to mathematical modelling
Mathematical models
An overview of the book
Some modelling approaches
Modelling for decision-making
Compartmental models
Exponential decay and radioactivity
Case Study: Detecting art forgeries
Case Study: Pacific rats colonise 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
Exercises for Chapter 2
Models of single populations
Exponential growth
Density dependent growth
Limited growth with harvesting
Case Study: Anchovy wipe-out
Case Study: How can 2 x 10[superscript 6] birds mean rare?
Discrete population growth and chaos
Time-delayed regulation
Case Study: Australian blowflies
Exercises for Chapter 3
Numerical solution of differential equations
Basic numerical schemes
Computer implementation using Maple and MATLAB
Exercises for Chapter 4
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 civilisations
Exercises for Chapter 5
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
Closed trajectories for the predator-prey
Case Study: Bacteria battle in the gut
Exercises for Chapter 6
Linearisation analysis
Linear theory
Applications of linear theory
Nonlinear theory
Applications of nonlinear theory
Exercises for Chapter 7
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
Exercises for Chapter 8
Formulating basic heat 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
Exercises for Chapter 9
Solving time dependent heat problems
The cooling coffee problem revisited
The hot water heater problem revisited
Case Study: It's hot and stuffy in the attic
Spontaneous combustion
Case Study: Fish and chips explode
Exercises for Chapter 10
Solving heat conduction problems
Boundary value problems
Heat loss through a wall
Case Study: Double glazing: What's it worth?
Insulating a water pipe
Cooling a computer chip
Exercises for Chapter 11
Introduction to partial differential equations
The heat conduction equation
Oscillating soil temperatures
Case Study: Detecting land mines
Lake pollution revisited
Exercises for Chapter 12
Differential equations
Properties of differential equations
Solution by inspection
First-order separable equations
First-order linear equations and integrating factors
Homogeneous equations
Inhomogeneous equations
Further mathematics
Linear algebra
Partial derivatives and Taylor expansions
Review of complex numbers
Hyperbolic functions
Integration using partial fractions
Notes on Maple and MATLAB
Brief introduction to Maple
Solving differential equations with Maple
Brief introduction to MATLAB
Solving differential equations with MATLAB
Units and scaling
Scaling differntial equations
SI Units