Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple and MATLAB, Second EditionCertain basic modeling skills can be applied to a wide variety of problems. It focuses on those mathematical techniques which are applicable to models involving differential equations. Models in three different areas are considered: growth and decay process, interacting populations and heating/cooling problems. The main mathematical technique is solving differential equations, while the range of applications and mathematical techniques presented provides a broad appreciation of this type of modeling. This book contains three general sections: Compartmental Models, Population Models and Heat Transfer Models. Within each section, the process of constructing a model is presented in full detail. Applications and case studies are integral to this text, and case studies are included throughout. This is a useful course text, and basic calculus and fundamental computing skills are required. |
Contents
Introduction to mathematical modelling 123792 | 1 |
Compartmental models | 17 |
Models of single populations | 61 |
Formulating interacting population models | 115 |
Phaseplane analysis | 163 |
Linearisation analysis | 197 |
Some improved population models | 223 |
Formulating basic heat models | 259 |
Solving heat conduction problems | 319 |
Introduction to partial differential equations | 355 |
A Differential equations | 383 |
B Further mathematics | 395 |
Notes on Maple | 409 |
| 415 | |
| 417 | |
| 423 | |
Other editions - View all
Mathematical Modelling with Case Studies: A Differential Equations Approach ... B. Barnes,G..R. Fulford No preview available - 2002 |
Mathematical Modelling with Case Studies: A Differential Equations Approach ... B. Barnes,G..R. Fulford No preview available - 2008 |
Common terms and phrases
a₁ alcohol approach arbitrary constant assume assumptions behaviour bloodstream blue army boundary conditions c₁ c₂ carrying capacity chain rule Chapter coefficient compartment compartmental diagram competing species consider curve decay decreasing describing differential equation disease dX dt dynamics eigenvalues eigenvectors epidemic equilibrium point equilibrium temperature Euler's method example exponential exponential growth Formulating Fourier's law function GI-tract given graph heat conduction heat fin heat flux heat loss herbivore illustrated in Figure increases initial conditions inits interaction k₁ lake linear linearised logistic equation logistic growth Lotka-Volterra equations mathematical model matrix nonlinear nullclines number of infectives number of susceptibles numerical solution obtain oscillations overview parameter values per-capita birth rate per-capita death rate phase-plane diagram phase-plane trajectories plot1 pollution population density positive constant possum predator predator-prey model predict prey problem radioactive rate of change rate of heat red army Section Skills developed tion variables word equation