Author | Britton, Nicholas Ferris. author |
---|---|
Title | Essential Mathematical Biology [electronic resource] / by Nicholas Ferris Britton |
Imprint | London : Springer London : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0049-2 |
Descript | XV, 335 p. 4 illus. online resource |
1. Single Species Population Dynamics -- 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 Poincarรฉ-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 Laplaceโs 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