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Modeling Differential Equations in Biology / Edition 1

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Overview

Given that a college level life science student will take only one additional calculus course after learning its very basics, what material should such a course cover? This book answers that question. It is based on a very successful one-semester course taught at Harvard and aims to teach students in the life sciences understanding the use of differential equations. It is enriched with illustrative examples from real papers. Necessary notions from linear algebra and partial differential equations are introduced as and when needed, and in the context of applications. Drawing on a very successful one-semester course at Harvard, this text aims to teach students in the life sciences how to use differential equations. It is enriched with illustrative examples from real papers. Necessary notions from mathematics are introduced as and when needed, and in the context of applications. Aimed at biologists wishing to understand mathematical modelling rather than just learning math methods.

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Editorial Reviews

Booknews
Taubes (mathematics, Harvard), including an article from current biology research literature as the source reading for each chapter, has created a hands-on text on using math in the biological sciences designed for students who have had calculus. Initial chapters cover the basics of ordinary differential equations with a single time derivative, focusing on equations with one and two unknowns, and considering phase plane analysis, equilibria, and stability. He then introduces partial differential equations, especially diffusion and advection equations, with additional chapters on traveling wave velocities, periodic solutions, fast and slow, estimating elapsed time, switches, testing for periodicity, and causes of chaos. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780130173256
  • Publisher: Prentice Hall
  • Publication date: 11/14/2000
  • Edition number: 1
  • Pages: 479
  • Product dimensions: 7.20 (w) x 9.20 (h) x 1.00 (d)

Table of Contents

Ch. 1 Introduction 1

Ch. 2 Exponential growth 6

Ch. 3 Introduction to differential equations 45

Ch. 4 Stability in a one-component system 64

Ch. 5 Systems of first-order differential equations 73

Ch. 6 Phase plane analysis 87

Ch. 7 Introduction to vectors 104

Ch. 8 Equilibrium in two-component, linear systems 127

Ch. 9 Stability in nonlinear systems 140

Ch. 10 Nonlinear stability revisited 147

Ch. 11 Matrix notation 173

Ch. 12 Remarks about Australian predators 178

Ch. 13 Introduction to advection 192

Ch. 14 Diffusion equations 216

Ch. 15 Two key properties of the advection and diffusion equations 226

Ch. 16 The no-trawling zone 246

Ch. 17 Separation of variables 259

Ch. 18 The diffusion equation and pattern formation 266

Ch. 19 Stability criterion 311

Ch. 20 Summary of advection/diffusion 318

Ch. 21 Traveling waves 351

Ch. 22 Traveling wave velocities 365

Ch. 23 Periodic solutions 375

Ch. 24 Fast and slow 393

Ch. 25 Estimating elapsed time 412

Ch. 26 Switches 416

Ch. 27 Testing for periodicity 430

Ch. 28 Causes of chaos 451

Extra exercises and solutions 481

Index 499

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