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Viser: Essential Mathematical Biology
Essential Mathematical Biology
Nicholas F. Britton
(2005)
Sprog: Engelsk
Detaljer om varen
- 1. Udgave
- Paperback: 335 sider
- Udgiver: Springer London, Limited (December 2005)
- ISBN: 9781852335366
2. Population Dynamics of Interacting Species.-
3. Infectious Diseases.-
4. Population Genetics and Evolution.-
5. Biological Motion.-
6. Molecular and Cellular Biology.-
7. Pattern Formation.-
8. Tumour Modelling.- Further Reading.- A. Some Techniques for Difference Equations.- A.1 First-order Equations.- A.1.1 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.1.1 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 Poincaré-Bendixson Theory.- B.3 Some Results and Techniques for rath 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.