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

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CRC Press, Mar 23, 2011 - Mathematics - 368 pages
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Focusing on growth and decay processes, interacting populations, and heating/cooling problems, Mathematical Modelling with Case Studies: A Differential Equations Approach using MapleTM and MATLABŪ, 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 MapleTM and MATLABŪ, 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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Contents

Introduction to mathematical modelling
1
Compartmental models
9
Models of single populations
51
Numerical solution of differential equations
83
Interacting population models
95
Phaseplane analysis
135
Linearisation analysis
169
Some extended population models
191
Solving heat conduction problems
263
Introduction to partial differential equations
289
Differential equations
309
Further mathematics
317
Notes on Maple and MATLAB
327
Units and scaling
335
References
339
Back cover
343

Formulating basic heat models
217
Solving time dependent heat problems
241

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