Springer大学数学图书：生物数学引论（影印版）

图书标准信息

• 作者 [美]尼古拉斯 著
• 出版社 清华大学出版社
• 出版时间 2009-11
• 版次 1
• ISBN 9787302214892
• 定价 46.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 335页
• 正文语种 英语

【内容简介】

　　《生物数学引论》由浅入深讲述生物数学基础理论，从最经典的问题入手，最后走向学科前沿和近年的热点问题；内容先进，讲述方法科学，简洁明了，易读性好。生物数学在应用数学中占有日益重要的地位，数学系培养的学生至少一部分人应当对这个领域有所了解。随着生命科学的迅速发展，生物数学也发展很快。
　　《生物数学引论》自身具有完整体系，在“微积分”、“代数”等基础课知识之外，读者不需要其他预备知识。
　　《生物数学引论》适合用作数学及生命科学高年级本科生相关课程教材或参考书。

【目录】

Contents
ListofFigures
1.SingleSpeciesPopulationDynamics
1.1Introduction
1.2LinearandNonlinearFirstOrderDiscreteTimeModels.
1.2.1TheBiologyofInsectPopulationDynamics
1.2.2AModelforInsectPopulationDynamicswithCompetition
1.3Differential-EquationModels
1.4EvolutionaryAspects
1.5HarvestingandFisheries
1.6Metapopulations
1.7DelayEffects
1.8Fibonaccis-Rabbits
1.9LeslieMatrices：Age-structuredPopulationsinDiscreteTime
110Euler-LotkaEquations
1.10.1DiscreteTime
1.10.2ContinuousTime
1.11TheMcKendrickApproachtoAgeStructure
112Conclusions

2.PopulationDynamicsofInteractingSpecies
2.1Introduction
22Host-parasitoidInteractions
2.3TheLotka-VolterraPrey-predatorEquations
2.4ModellingthePredatorFunctionalResponse
2.5Competition.
2.6EcosystemsModelling
2.7InteractingMetapopulations
2.7.1Competition
2.7.2Predation
2.7.3Predator-mediatedCoexistenceofCompetitors
2.7.4EffectsofHabitatDestruction
2.8Conclusions

3.InfectiousDiseases
3.1Introduction
3.2TheSimpleEpidemicandSISDiseases
3.3SIREpidemics
3.4SIREndemics
3.4.1NoDisease-relatedDeath
3.4.2IncludingDisease-relatedDeath
3.5EradicationandControl
3.6Age-structuredPopulations
3.6.1TheEquations
3.6.2SteadyState
3.7Vector-borneDiseases
3.8BasicModelforMacroparasiticDiseases
3.9EvolutionaryAspects
3.10Conclusions

4.PopulationGeneticsandEvolution
4.1Introduction
4.2MendelianGeneticsinPopulationswithNon-overlappingGenerations
4.3SelectionPressure
4.4SelectioninSomeSpecialCases
4.4.1SelectionforaDominantAllele
4.4.2SelectionforaRecessiveAllele
4.4.3SelectionagainstDominantandRecessiveAlleles
4.4.4TheAdditiveCase
4.5AnalyticalApproachforWeakSelection
4.6TheBalanceBetweenSelectionandMutation
4.7WrightsAdaptiveTopography
4.8EvolutionoftheGeneticSystem
4.9GameTheory
4.10ReplicatorDynamics
4.11Conclusions

5.BiologicalMotion
5.1Introduction
5.2MacroscopicTheoryofMotion;AContinuumApproach
5.2.1GeneralDerivation
5.2.2SomeParticularCases
5.3DirectedMotion，orTaxis
5.4SteadyStateEquationsandTransitTimes
5.4.1SteadyStateEquationsinOneSpatialVariable
5.4.2TransitTimes
5.4.3MacrophagesvsBacteria
5.5BiologicalInvasions：AModelforMuskratDispersal
5.6TravellingWaveSolutionsofGeneralReaction-diffusionEquations
5.6.1Node-saddleOrbits(theMonostableEquation)
5.6.2Saddle-saddleOrbits(theBistableEquation)
5.7TravellingWaveSolutionsofSystemsofReaction-diffusion
Equations：SpatialSpreadofEpidemics
5.8Conclusions

6.MolecularandCellularBiology
6.1Introduction
6.2BiochemicalKinetics
6.3MetabolicPathways
6.3.1ActivationandInhibition
6.3.2CooperativePhenomena
6.4NeuralModelling
6.5ImmunologyandAIDS
6.6Conclusions

7.PatternFormation
7.1Introduction
7.2TuringInstability
7.3TuringBifurcations
7.4Activator-inhibitorSystems
7.4.1ConditionsforTuringInstability
7.4.2Short-rangeActivation，Long-rangeInhibition
7.4.3DoActivator-inhibitorSystemsExplainBiologicalPatternFormation?
7.5BifurcationswithDomainSize
7.6IncorporatingBiologicalMovement
7.7MechanochemicalModels
7.8Conclusions

8.TumourModelling
8.1Introduction
8.2PhenomenologicalModels
8.3Nutrients：theDiffusion-limitedStage
8.4MovingBoundaryProblems
8.5GrowthPromotersandInhibitors
8.6Vascularisation
8.7Metastasis
8.8ImmuneSystemResponse
8.9Conclusions

FurtherReading
A.SomeTechniquesforDifferenceEquations
A.IFirst-orderEquations
A.I.1GraphicalAnalysis
A.1.2Linearisation
A.2BifurcationsandChaosforFirst-orderEquations
A.2.1Saddle-nodeBifurcations
A.2.2TranscriticalBifurcations
A.2.3PitchforkBifurcations
A.2.4Period-doublingorFlipBifurcations
A.3SystemsofLinearEquations：JuryConditions
A.4SystemsofNonlinearDifferenceEquations
A.4.1LinearisationofSystems
A.4.2BifurcationforSystems
B.SomeTechniquesforOrdinaryDifferentialEquations
B.1First-orderOrdinaryDifferentialEquations
B.I.1GeometricAnalysis
B.1.2Integration
B.1.3Linearisation
B.2Second-orderOrdinaryDifferentialEquations
B.2.1GeometricAnalysis(PhasePlane)
B.2.2Linearisation
B.2.3Poincard-BendixsonTheory
B.3SomeResultsandTechniquesforruthOrderSystems
B.3.1Linearisation
B.3.2LyapunovFunctions
B.3.3SomeMiscellaneousFacts
B.4BifurcationTheoryforOrdinaryDifferentialEquations
B.4.1BifurcationswithEigenvalueZero
B.4.2HopfBifurcations
C.SomeTechniquesforPartialDifferentialEquations
C.1First-orderPartialDifferentialEquationsandCharacteristics
C.2SomeResultsandTechniquesfortheDiffusionEquation
C.2.1TheFundamentalSolution
C.2.2ConnectionwithProbabilities
C.2.3OtherCoordinateSystems
C.3SomeSpectralTheoryforLaplacesEquation
C.4SeparationofVariablesinPartialDifferentialEquations
C.5SystemsofDiffusionEquationswithLinearKinetics
C.6SeparatingtheSpatialVariablesfromEachOther
D.Non-negativeMatrices
D.1Perron-FrobeniusTheory
E.HintsforExercises
Index