Rent 9780470525876 | Mathematical Methods in Biology | Logan, J. David; Wolesensky, William @knetbooks.com

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Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs, and TractsMathematical Methods in BiologyJ. David Logan & William R. WolesenskyA one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciencesHighlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals ... MOREthe growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory.The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic.In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLABr, but can also be replicated using other software packages, including R, Mathematicar, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study.Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics.

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 stochastic differential equations. The book focuses mostly in one area of the life sciences, namely, theoretical ecology. Ecology has become extremely quantitative, and the mathematical techniques used in ecology are applicable to most other areas in the life sciences. Ecology provides an especially accessible context for study by mathematics majors. Moreover, the authors chose ecology for the book's motivations and examples in light of their own interests and research in the area. Additional topical coverage includes an introduction to ecological modeling, population dynamics for single species, structure and interacting populations, interactions in continuous time, concepts of probability, statistical inference, and stochastic processes.

Mathematics Method in Biology uniquely covers both deterministic and probabilistic models, including algorithms in the MATLAB platform. The book focuses mostly in one area of the life sciences, focusing mainly on theoretical ecology.

A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences

Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory.

The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic.

In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB�, but can also be replicated using other software packages, including R, Mathematica�, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study.

Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics.

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Preface	p. xi
Introduction to Ecological Modeling	p. 1
Mathematical Models	p. 1
Rates of Change	p. 6
Taylor Polynomials	p. 9
Foraging Theory	p. 12
Balance Laws	p. 18
Temperature in the Environment	p. 25
Heat Transfer	p. 25
Dynamic Temperatures	p. 27
Development Rate	p. 32
Dimensionless Variables	p. 37
Descriptive Statistics	p. 40
Regression and Curve Fitting	p. 44
Reference Notes	p. 51
Population Dynamics for Single Species	p. 55
Laws of Population Dynamics	p. 56
Continuous-Time Models	p. 60
Qualitative Analysis of Population Models	p. 65
Dynamics of Predation	p. 73
Discrete-Time Models	p. 81
Equilibria, Stability, and Chaos	p. 87
Reference Notes	p. 96
Structure and Interacting Populations	p. 99
Structure: Juveniles and Adults	p. 99
Structured Linear Models	p. 102
Sensitivity and Elasticity	p. 107
Nonlinear Interactions	p. 115
Appendix: Matrices	p. 124
Matrix Notation and Algebra	p. 124
Linear Algebraic Equations	p. 130
The Eigenvalue Problem	p. 135
Reference Notes	p. 141
Interactions in Continuous Time	p. 143
Interacting Populations	p. 143
Phase Plane Analysis	p. 151
Linear Systems	p. 158
Nonlinear Systems	p. 165
Bifurcation	p. 173
Rosenzweig-MacArthur Model	p. 177
Reference Notes	p. 186
Concepts of Probability	p. 189
Introductory Examples and Definitions	p. 189
The Hardy-Weinberg Law	p. 199
Continuous Random Variables	p. 202
The Normal Distribution	p. 203
General Random Variables	p. 206
Predation with a Random Search	p. 212
Central Limit Theorem	p. 216
Discrete Random Variables	p. 220
Likelihood	p. 226
Joint Probability Distributions	p. 232
Covariance and Correlation	p. 238
Covariance	p. 238
Covariance Matrix	p. 241
Reference Notes	p. 243
Statistical Inference	p. 247
Introduction	p. 248
Interval Analysis	p. 250
Known Variance	p. 250
The Gamma Distribution	p. 254
The Sample Variance	p. 257
The Mean with Unknown Variance	p. 258
Estimating Proportions	p. 260
The Chi-Squared Test	p. 263
Hypothesis Testing	p. 267
Bootstrap Methods	p. 275
Nonparametric Bootstrapping	p. 277
Parametric Bootstrapping	p. 286
Permutation Methods	p. 289
Reference Notes	p. 300
Stochastic Processes	p. 303
Introduction	p. 303
Randomizing Discrete Dynamics	p. 308
Environmental and Demographic Stochasticity	p. 314
Random Walk	p. 319
Birth Processes	p. 323
Linear Differential Equations	p. 323
Simple Birth Process	p. 325
Interevent Times and Simulation	p. 329
Stochastic Differential Equations	p. 331
Examples	p. 331
The Wiener Process	p. 332
Stochastic Differential Equations	p. 337
SDEs from Markov Models	p. 342
Solving SDEs	p. 347
The It&ohat; Identity	p. 347
Stochastic Integrals	p. 349
Solving SDEs	p. 350
The Fokker-Planck Equation	p. 352
Reference Notes	p. 358
A. Hints and Solutions to Exercises	p. 361
Index	p. 415
Table of Contents provided by Ingram. All Rights Reserved.

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.

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