Mathematical Methods in Biology (Pure & Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

Mathematik trifft Biologie: Dieser Band lotet ein spannendes Grenzgebiet aus. Er informiert nicht nur ber Grundlagen, sondern auch ber moderne Spezialthemen wie Populationsdynamik, Ftterungstheorie und Theorie der Lebensgeschichte und enthlt Material, dass Sie ansonsten kaum in der Literatur finden. Zunchst vermitteln die Autoren das notwendige mathematische Rstzeug (biologische Modellierung, Infinitesimalrechnung, Differenzialgleichungen, dimensionslose Variable, deskriptive Statistik). Anschlieend untersuchen sie diskrete und kontinuierliche Standardmodelle (Matrizenalgebra ebenso wie Differenzen- und Differenzialgleichungen). Im letzten Teil geht es um Wahrscheinlichkeitsrechnung, Statistik, stochastische Methoden, Bootstrapping und stochastische Differenzialgleichungen. J. David Logan, PhD, is Willa Cather Professor of Mathematics at the University of Nebraska-Lincoln. He has written more than eighty research articles in his areas of research interest, which include mathematical physics, combustion and detonation, hydrogeology, and mathematical biology. Dr. Logan is the author of Applied Mathematics, Third Edition and An Introduction to Nonlinear Partial Differential Equations, Second Edition, both published by Wiley. William R. Wolesensky, PhD, is Associate Professor in the Department of Mathematics at Doane College. Dr. Wolesensky has written numerous journal articles on the use of mathematical modeling techniques in scientific research. Preface. 1. Introduction To Ecological Modeling. 1.1 Mathematical Models. 1.2 Rates of Change. 1.3 Balance Laws. 1.4 Temperature in the Environment. 1.5 Dimensionless Variables. 1.6 Descriptive Statistics. 1.7 Regression and Curve Fitting. 1.8 Reference Notes. 2. Population Dynamics for Single Species. 2.1 Laws of Population Dynamics. 2.2 Continuous Time Models. 2.3 Qualitative Analysis of Population Models. 2.4 Dynamics of Predation. 2.5 Discrete Time Models. 2.6 Equilibria, Stability, and Chaos. 2.7 Reference Notes. 3. Structure and Interacting Populations. 3.1 Structure--Juveniles and Adults. 3.2 Structured Linear Models. 3.3 Nonlinear Interactions. 3.4 Appendix--Matrices. 3.5 Reference Notes. 4. Interactions in Continuous Time. 4.1 Interacting Populations. 4.2 Phase Plane Analysis. 4.3 Linear Systems. 4.4 Nonlinear Systems. 4.5 Bifurcation. 4.6 Reference Notes. 5. Concepts of Probability. 5.1 Introductory Examples and Definitions. 5.2 The Hardy-Weinberg Law. 5.3 Continuous Random Variables. 5.4 Discrete Random Variables. 5.5 Joint Probability Distributions. 5.6 Covariance and Correlation. 5.7 Reference Notes. 6. Statistical Inference. 6.1 Introduction. 6.2 Interval Analysis. 6.3 Estimating Proportions. 6.4 The Chi-Squared Test. 6.5 Hypothesis Testing. 6.6 Bootstrap Methods. 6.7 Reference Notes. 7. Stochastic Processes. 7.1 Introduction. 7.2 Randomizing Discrete Dynamics. 7.3 Random Walk. 7.4 Birth Processes. 7.5 Stochastic Differential Equations. 7.6 SDEs from Markov Models. 7.7 Solving SDEs. 7.8 The Fokker-Planck Equation. 7.9 Reference Notes. A. Hints and Solutions to Exercises