Mathematical modelling with case studies: a differential equation approach using Maple
Choice Reviews Online · 2003
INTRODUCTION TO MATHEMATICAL MODELINGMathematical ModelsAn Overview of the BookSome Modelling AproachesThe Cyclic ProcessModelling for Decision-MakingPART 1: INTRODUCTION TO COMPARTMENTAL MODELSCOMPARTMENTAL MODELSIntroductionExponential Decay and RadioactivityCase Study: Detecting Art ForgeriesCase Study: Pacific rats Colonise New ZealandLake Pollution ModelsCase Study: Lake Brley riffinDrug Assimilation into the BloodCase Study: Dull, Dizzy, or Dead?Cascades of CompartmentsFirst-Order Linear DEsExercisesMODELS OF SINGLE POPULATIONSExponential GrowthLimited GrowthLimited Growth with HarvestingCase Study: Anchovy Wipe-OutCase Study: How can 2 x 10(6) Birds Mean Rare?Time-Delayed RegulationCase Study: Australian BlowfliesExercisesNUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONSIntroductionBasic Numerical SchemesComputer ImplementationInstabilityDiscussionExercisesPART II: MODELS OF INTERACTING POPULATIONSFORMULATING MODELSIntroductionCase Study: Nile Perch CatastrophePredators and PreyCompeting SpeciesCase Study: Aggressive Protection of Lerps and NymphsAn Epidemic Model for InfluenzaSimple Model of a BattleExercisesPHASE-PLANE ANALYSISIntroductionAnalysis of a Predator-Prey ModelAnalysis of Competing Species ModelsAnalysis of an Epidemic ModelAnalysis of a Battle ModelThe Predator-Prey Model RevisitedExercisesLINEARIZATION ANALYSISIntroductionLinear TheoryApplications of Linear TheoryNonlinear TheoryApplications of Nonlinear TheoryExercisesSOME IMPROVED POPULATION MODELSIntroductionCase Study: Competition, Predation, and DiversityExtended Predator-Prey ModelCase Study: Lemming Mass SuicidesCase Study: Prickly-Pear Meets its MothCase Study: Geese Defy Mathematical ConventionCase Study: Possums Threaten New Zealand CowsExercisesPART III: MODELS OF HEATING AND COOLINGFORMULATING BASIC MODELSIntroductionSome Basic Physical LawsModel for a Hot Water HeaterHeat Conduction and Fourier's LawHeat Conduction through a WallRadial Heat conductionHeat FinsExercisesSOLVING TIME-DEPENDENT PROBLEMSThe Cooling Coffee Problem RevisitedThe Hot Ware Heater Problem RevisitedCase Study: It's Hot and Stufy in the AtticSpontaneous CombustionCase Study: Fish and Chips ExplodeExercisesSOLVING HEAT CONDUCTION PROBLEMSBoundary Condition ProblemsHeat Loss through a WallCase Study: Double Glazing: What's it Worth?Insulating a Water PipeCooling a Computer chipExercisesPART IV: MODELS WITH PARTIAL DIFFERENTIAL EQUATIONSINTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONSThe Heat EquationOscillating Soil TemperaturesCase Study: Detecting Land MinesLake Pollution RevisitedExercisesAPPENDICESDifferential EquationsFurther MathematicsNotes on MapleA Brief Introduction to mapleSI UnitsBibliography