Mathematical modelling with case studies : a differential equations approach using Maple and MATLAB /

Mathematical modelling with case studies : a differential equations approach using Maple and MATLAB /

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Bibliographic Details
Author / Creator:Barnes, Belinda, 1959- Dr.
Edition:2nd ed.
Imprint:Boca Raton : CRC Press, c2009.
Description:ix, 349 p. : ill. ; 26 cm.
Language:English
Subject:
Maple (Computer file)
Maple (Computer file)
Differential equations -- Mathematical models.
Differential equations -- Data processing.
Mathematical models.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/7680228
Hidden Bibliographic Details
Other authors / contributors:Fulford, Glenn.
ISBN:9781420083484 (hardcover : alk. paper)
1420083481 (hardcover : alk. paper)
Notes:"A Chapman & Hall book."
Includes bibliographical references (p. 339-342) and index.
Table of Contents:
  • Preface
  • Acknowledgements
  • 1. Introduction to mathematical modelling
  • 1.1. Mathematical models
  • 1.2. An overview of the book
  • 1.3. Some modelling approaches
  • 1.4. Modelling for decision-making
  • 2. Compartmental models
  • 2.1. Introduction
  • 2.2. Exponential decay and radioactivity
  • 2.3. Case Study: Detecting art forgeries
  • 2.4. Case Study: Pacific rats colonise New Zealand
  • 2.5. Lake pollution models
  • 2.6. Case Study: Lake Burley Griffin
  • 2.7. Drug assimilation into the blood
  • 2.8. Case Study: Dull, dizzy or dead?
  • 2.9. Cascades of compartments
  • 2.10. First-order linear DEs
  • 2.11. Equilibrium points and stability
  • 2.12. Case Study: Money, money, money makes the world go around
  • 2.13. Exercises for Chapter 2
  • 3. Models of single populations
  • 3.1. Exponential growth
  • 3.2. Density dependent growth
  • 3.3. Limited growth with harvesting
  • 3.4. Case Study: Anchovy wipe-out
  • 3.5. Case Study: How can 2 x 10[superscript 6] birds mean rare?
  • 3.6. Discrete population growth and chaos
  • 3.7. Time-delayed regulation
  • 3.8. Case Study: Australian blowflies
  • 3.9. Exercises for Chapter 3
  • 4. Numerical solution of differential equations
  • 4.1. Introduction
  • 4.2. Basic numerical schemes
  • 4.3. Computer implementation using Maple and MATLAB
  • 4.4. Instability
  • 4.5. Discussion
  • 4.6. Exercises for Chapter 4
  • 5. Interacting population models
  • 5.1. Introduction
  • 5.2. An epidemic model for influenza
  • 5.3. Predators and prey
  • 5.4. Case Study: Nile Perch catastrophe
  • 5.5. Competing species
  • 5.6. Case Study: Aggressive protection of lerps and nymphs
  • 5.7. Model of a battle
  • 5.8. Case Study: Rise and fall of civilisations
  • 5.9. Exercises for Chapter 5
  • 6. Phase-plane analysis
  • 6.1. Introduction
  • 6.2. Phase-plane analysis of epidemic model
  • 6.3. Analysis of a battle model
  • 6.4. Analysis of a predator-prey model
  • 6.5. Analysis of competing species models
  • 6.6. Closed trajectories for the predator-prey
  • 6.7. Case Study: Bacteria battle in the gut
  • 6.8. Exercises for Chapter 6
  • 7. Linearisation analysis
  • 7.1. Introduction
  • 7.2. Linear theory
  • 7.3. Applications of linear theory
  • 7.4. Nonlinear theory
  • 7.5. Applications of nonlinear theory
  • 7.6. Exercises for Chapter 7
  • 8. Some extended population models
  • 8.1. Introduction
  • 8.2. Case Study: Competition, predation and diversity
  • 8.3. Extended predator-prey model
  • 8.4. Case Study: Lemming mass suicides?
  • 8.5. Case Study: Prickly-pear meets its moth
  • 8.6. Case Study: Geese defy mathematical convention
  • 8.7. Case Study: Possums threaten New Zealand cows
  • 8.8. Exercises for Chapter 8
  • 9. Formulating basic heat models
  • 9.1. Introduction
  • 9.2. Some basic physical laws
  • 9.3. Model for a hot water heater
  • 9.4. Heat conduction and Fourier's law
  • 9.5. Heat conduction through a wall
  • 9.6. Radial heat conduction
  • 9.7. Heat fins
  • 9.8. Exercises for Chapter 9
  • 10. Solving time dependent heat problems
  • 10.1. The cooling coffee problem revisited
  • 10.2. The hot water heater problem revisited
  • 10.3. Case Study: It's hot and stuffy in the attic
  • 10.4. Spontaneous combustion
  • 10.5. Case Study: Fish and chips explode
  • 10.6. Exercises for Chapter 10
  • 11. Solving heat conduction problems
  • 11.1. Boundary value problems
  • 11.2. Heat loss through a wall
  • 11.3. Case Study: Double glazing: What's it worth?
  • 11.4. Insulating a water pipe
  • 11.5. Cooling a computer chip
  • 11.6. Exercises for Chapter 11
  • 12. Introduction to partial differential equations
  • 12.1. The heat conduction equation
  • 12.2. Oscillating soil temperatures
  • 12.3. Case Study: Detecting land mines
  • 12.4. Lake pollution revisited
  • 12.5. Exercises for Chapter 12
  • A. Differential equations
  • A.1. Properties of differential equations
  • A.2. Solution by inspection
  • A.3. First-order separable equations
  • A.4. First-order linear equations and integrating factors
  • A.5. Homogeneous equations
  • A.6. Inhomogeneous equations
  • B. Further mathematics
  • B.1. Linear algebra
  • B.2. Partial derivatives and Taylor expansions
  • B.3. Review of complex numbers
  • B.4. Hyperbolic functions
  • B.5. Integration using partial fractions
  • C. Notes on Maple and MATLAB
  • C.1. Brief introduction to Maple
  • C.2. Solving differential equations with Maple
  • C.3. Brief introduction to MATLAB
  • C.4. Solving differential equations with MATLAB
  • D. Units and scaling
  • D.1. Scaling differntial equations
  • D.2. SI Units
  • References
  • Index

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