圖書信息
出版社: 清華大學出版社; 第1版 (2009年
外文書名: Essential Mathematical Biology
叢書名: Springer 大學數學圖書
平裝: 335頁
正文語種: 英語
開本: 16
ISBN: 9787302214892
條形碼: 9787302214892
尺寸: 24.2 x 17.2 x 1.8 cm
重量: 499 g
作者簡介
作者：(美國)尼古拉斯(Nicholas F.Britton)
內容簡介
《生物數學引論》由淺入深講述生物數學基礎理論，從最經典的問題入手，最後走向學科前沿和近年的熱點問題；內容先進，講述方法科學，簡潔明了，易讀性好。生物數學在套用數學中占有日益重要的地位，數學系培養的學生至少一部分人應當對這個領域有所了解。隨著生命科學的迅速發展，生物數學也發展很快。
《生物數學引論》自身具有完整體系，在“微積分”、“代數”等基礎課知識之外，讀者不需要其他預備知識。
《生物數學引論》適合用作數學及生命科學高年級本科生相關課程教材或參考書。
目錄
Contents
List of Figures
1. Single Species Population Dynamics
1.1 Introduction
1.2 Linear and Nonlinear First Order Discrete Time Models.
1.2.1 The Biology of Insect Population Dynamics
1.2.2 A Model for Insect Population Dynamics with Competition
1.3 Differential-Equation Models
1.4 EvolutionaryAspects
1.5 Harvesting and Fisheries
1.6 Metapopulations
1.7 Delay Effects
1.8Fibonacci's-Rabbits
1.9 Leslie Matrices: Age-structured Populations in Discrete Time
1 10 Euler-Lotka Equations
1.10.1 Discrete Time
1.10.2 Continuous Time
1.11 The McKendrick Approach to Age Structure
1 12 Conclusions
2. Population Dynamics of Interacting Species
2.1 Introduction
2 2 Host-parasitoid Interactions
2.3 The Lotka-Volterra Prey-Predator Equations
2.4 Modelling the Predator Functional Response
2.5 Competition.
2.6 Ecosystems Modelling
2.7 Interacting Metapopulations
2.7.1 Competition
2.7.2 Predation
2.7.3 Predator-mediated coexistence of Competitors
2.7.4 Effects of Habitat Destruction
2.8 Conclusions
3. Infectious Diseases
3.1 Introduction
3.2 The Simple Epidemic and SIS Diseases
3.3 SIR Epidemics
3.4 SIR Endemics
3.4.1 No Disease-related Death
3.4.2 Including Disease-related Death
3.5 Eradication and Control
3.6 Age-structured Populations
3.6.1 The Equations
3.6.2 Steady State
3.7 Vector-borne Diseases
3.8 Basic Model for Macroparasitic Diseases
3.9 Evolutionary Aspects
3.10 Conclusions
4. Population Genetics and Evolution
4.1 Introduction
4.2 Mendelian Genetics in Populations with Non-overlapping Generations
4.3 Selection Pressure
4.4 Selection in Some Special Cases
4.4.1 Selection for a Dominant Allele
4.4.2 Selection for a recessive Allele
4.4.3 Selection against Dominant and Recessive Alleles
4.4.4 The Additive Case
4.5 Analytical Approach for Weak Selection
4.6 The Balance Between Selection and Mutation
4.7 Wright's Adaptive Topography
4.8 Evolution of the Genetic System
4.9 Game Theory
4.10 Replicator Dynamics
4.11 Conclusions
5. Biological Motion
5.1 Introduction
5.2 macroscopic Theory of Motion; A Continuum Approach
5.2.1 General Derivation
5.2.2 Some Particular Cases
5.3 Directed Motion, or Taxis
5.4 Steady State Equations and Transit Times
5.4.1 Steady State Equations in One Spatial Variable
5.4.2 Transit Times
5.4.3 Macrophages vs Bacteria
5.5 Biological Invasions: A Model for muskrat Dispersal
5.6 Travelling Wave Solutions of General Reaction-diffusion Equations
5.6.1 Node-saddle Orbits (the Monostable Equation)
5.6.2 Saddle-saddle Orbits (the Bistable Equation)
5.7 Travelling Wave Solutions of Systems of Reaction-diffusion
Equations: Spatial Spread of Epidemics
5.8 Conclusions
6. Molecular and Cellular Biology
6.1 Introduction
6.2 Biochemical Kinetics
6.3 Metabolic Pathways
6.3.1 Activation and Inhibition
6.3.2 Cooperative Phenomena
6.4 Neural Modelling
6.5 Immunology and AIDS
6.6 Conclusions
7. Pattern Formation
7.1 Introduction
7.2 Turing Instability
7.3 Turing Bifurcations
7.4 Activator-inhibitor Systems
7.4.1 Conditions for Turing Instability
7.4.2 Short-range Activation, Long-range Inhibition
7.4.3 Do Activator-inhibitor Systems Explain Biological Pattern Formation?
7.5 Bifurcations with Domain Size
7.6 Incorporating Biological Movement
7.7 Mechanochemical Models
7.8 Conclusions
8. Tumour Modelling
8.1 Introduction
8.2 Phenomenological Models
8.3 Nutrients: the Diffusion-limited Stage
8.4 Moving Boundary Problems
8.5 Growth Promoters and Inhibitors
8.6 Vascularisation
8.7 Metastasis
8.8 Immune System Response
8.9 Conclusions
Further Reading
A. Some Techniques for Difference Equations
A.I First-order Equations
A.I.1 Graphical Analysis
A.1.2 Linearisation
A.2 Bifurcations and Chaos for First-order Equations
A.2.1 Saddle-node Bifurcations
A.2.2 Transcritical Bifurcations
A.2.3 pitchfork Bifurcations
A.2.4 Period-doubling or Flip Bifurcations
A.3 Systems of Linear Equations: Jury Conditions
A.4 Systems of Nonlinear Difference Equations
A.4.1 Linearisation of Systems
A.4.2 Bifurcation for Systems
B. Some Techniques for Ordinary Differential Equations
B.1 First-order Ordinary Differential Equations
B.I.1 Geometric Analysis
B.1.2 Integration
B.1.3 Linearisation
B.2 Second-order Ordinary Differential Equations
B.2.1 Geometric Analysis (Phase Plane)
B.2.2 Linearisation
B.2.3 Poincard-Bendixson Theory
B.3 Some Results and Techniques for ruth Order Systems
B.3.1 Linearisation
B.3.2 Lyapunov Functions
B.3.3 Some Miscellaneous Facts
B.4 Bifurcation Theory for Ordinary Differential Equations
B.4.1 Bifurcations with Eigenvalue Zero
B.4.2 Hopf Bifurcations
C. Some Techniques for Partial Differential Equations
C.1 First-order Partial Differential Equations and Characteristics
C.2 Some Results and Techniques for the Diffusion Equation
C.2.1 The Fundamental Solution
C.2.2 Connection with Probabilities
C.2.3 Other Coordinate Systems
C.3 Some Spectral Theory for Laplace's Equation
C.4 Separation of Variables in Partial Differential Equations
C.5 Systems of Diffusion Equations with Linear Kinetics
C.6 Separating the Spatial Variables from Each Other
D. Non-negative Matrices
D.1 Perron-Frobenius Theory
E. Hints for Exercises
Index
