Mathematical Methods in Biology

Name: Mathematical Methods in Biology
Price: 78.62 USD
Availability: InStock
ISBN: 9780470525876

ISBN-10: 0470525878

ISBN-13: 9780470525876

Edition: 2009

Authors: J. David Logan, William Wolesensky

List price: $142.00

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Description:

The last several years has witnessed a revolution in the connections between mathematics and biology, and this book differs from most others on the topic in that it covers both deterministic and probabilistic models. The first chapter is a long introduction and review of ideas about biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The next three chapters examine standard discrete and continuous models using difference and differential equations, and matrix algebra (there is a long appendix in Chapter 3 on matrices). The final three chapters cover probability, statistics, and stochastic processes, including bootstrap methods and…

Book details

List price: $142.00
Copyright year: 2009
Publisher: John Wiley & Sons Canada, Limited
Publication date: 8/17/2009
Binding: Paperback
Pages: 436
Size: 6.20" wide x 9.20" long x 0.90" tall
Weight: 1.298
Language: English



Preface



Introduction to Ecological Modeling



Mathematical Models



Rates of Change



Taylor Polynomials



Foraging Theory



Balance Laws



Temperature in the Environment



Heat Transfer



Dynamic Temperatures



Development Rate



Dimensionless Variables



Descriptive Statistics



Regression and Curve Fitting



Reference Notes



Population Dynamics for Single Species



Laws of Population Dynamics



Continuous-Time Models



Qualitative Analysis of Population Models



Dynamics of Predation



Discrete-Time Models



Equilibria, Stability, and Chaos



Reference Notes



Structure and Interacting Populations



Structure: Juveniles and Adults



Structured Linear Models



Sensitivity and Elasticity



Nonlinear Interactions



Appendix: Matrices



Matrix Notation and Algebra



Linear Algebraic Equations



The Eigenvalue Problem



Reference Notes



Interactions in Continuous Time



Interacting Populations



Phase Plane Analysis



Linear Systems



Nonlinear Systems



Bifurcation



Rosenzweig-MacArthur Model



Reference Notes



Concepts of Probability



Introductory Examples and Definitions



The Hardy-Weinberg Law



Continuous Random Variables



The Normal Distribution



General Random Variables



Predation with a Random Search



Central Limit Theorem



Discrete Random Variables



Likelihood



Joint Probability Distributions



Covariance and Correlation



Covariance



Covariance Matrix



Reference Notes



Statistical Inference



Introduction



Interval Analysis



Known Variance



The Gamma Distribution



The Sample Variance



The Mean with Unknown Variance



Estimating Proportions



The Chi-Squared Test



Hypothesis Testing



Bootstrap Methods



Nonparametric Bootstrapping



Parametric Bootstrapping



Permutation Methods



Reference Notes



Stochastic Processes



Introduction



Randomizing Discrete Dynamics



Environmental and Demographic Stochasticity



Random Walk



Birth Processes



Linear Differential Equations



Simple Birth Process



Interevent Times and Simulation



Stochastic Differential Equations



Examples



The Wiener Process



Stochastic Differential Equations



SDEs from Markov Models



Solving SDEs



The It&ohat; Identity



Stochastic Integrals



Solving SDEs



The Fokker-Planck Equation



Reference Notes


A. Hints and Solutions to Exercises


Index