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Biology in Time and Space: A Partial Differential Equation Modeling Approach [Mīkstie vāki]

  • Formāts: Paperback / softback, 314 pages, height x width: 254x178 mm, weight: 575 g
  • Sērija : Pure and Applied Undergraduate Texts
  • Izdošanas datums: 30-Sep-2021
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 1470454289
  • ISBN-13: 9781470454289
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  • Mīkstie vāki
  • Cena: 113,24 €
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  • Formāts: Paperback / softback, 314 pages, height x width: 254x178 mm, weight: 575 g
  • Sērija : Pure and Applied Undergraduate Texts
  • Izdošanas datums: 30-Sep-2021
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 1470454289
  • ISBN-13: 9781470454289
Citas grāmatas par šo tēmu:
Keener presents an undergraduate textbook on using mathematics to begin to tell the story of how biological objects do what they do, such as communicate, make structures, make measurements and decisions, and search for food. Focusing on the broad areas of population biology and cellular biology, he consider such topics as conservation: learning how to count, realizations of a diffusion process, the Bistable Equation: derivations and analysis, advection with diffusion, dispersal-renewal theory, and collective behavior. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)

Recenzijas

This book tells the story of living processes that change in time and space. Driven by scientific inquiry, methods from partial differential equations, stochastic processes, dynamical systems, and numerical methods are brought to bear on the subject, and their exposition seems effortless in the pursuit of deeper biological understanding. With subjects ranging from spruce budworm populations to calcium dynamics and from tiger bush patterns to collective behavior, this is a must-read for anyone who is serious about modern mathematical biology."" Mark Lewis, University of Alberta.

""Prof. Keener is one of the Great Minds in Math Biology who has trained generations of fine scientists and mathematicians over the years."" Leah Edelstein-Keshet, University of British Columbia.

""This is a fantastic book for those of us who teach mathematical modelling of spatiotemporal phenomena in biology, and for anyone who wishes to move into the field. It guides the reader on how one should tackle the art of modelling and, in a very systematic and natural way, introduces many of the necessary mathematical and computational approaches, seamlessly integrating them with the biology. It is a pleasure to read."" Philip Maini, University of Oxford

""Mathematical Biology has few foundational texts. But this is one."" Michael C. Reed, Duke University

Preface xi
Chapter 1 Background Material 1(38)
1.1 Multivariable Calculus
1(4)
1.2 Ordinary Differential Equations
5(10)
1.3 Stochastic Processes
15(13)
Exercises
28(11)
Chapter 2 Conservation- Learning How to Count 39(8)
2.1 The Conservation Law
39(2)
2.2 Examples of Flux-How Things Move
41(3)
Exercises
44(3)
Chapter 3 The Diffusion Equation- Derivations 47(12)
3.1 Discrete Boxes
47(1)
3.2 A Random Walk
48(4)
3.3 The Cable Equation
52(4)
Exercises
56(3)
Chapter 4 Realizations of a Diffusion Process 59(16)
4.1 Following Individual Particles
59(2)
4.2 Other Features of Brownian Particle Motion
61(4)
4.3 Following Several Particles
65(1)
4.4 Effective Diffusion
66(3)
4.5 An Agent-Based Approach
69(2)
Exercises
71(4)
Chapter 5 Solutions of the Diffusion Equation 75(20)
5.1 On an Infinite Domain
75(2)
5.2 On the Semi-infinite Line
77(2)
5.3 With Boundary Conditions
79(2)
5.4 Separation of Variables
81(3)
5.5 Numerical Methods
84(3)
5.6 Comparison Theorems
87(1)
5.7 FRAP
88(3)
Exercises
91(4)
Chapter 6 Diffusion and Reaction 95(36)
6.1 Birth-Death with Diffusion
95(6)
6.2 Growth with a Carrying Capacity-Fisher's Equation
101(12)
6.3 Resource Consumption
113(3)
6.4 Spread of Rabies-SIR with Diffusion
116(3)
6.5 Extras: Facilitated Diffusion
119(6)
Exercises
125(6)
Chapter 7 The Bistable Equation-Part I: Derivations 131(10)
7.1 Spruce Budworm
131(3)
7.2 Wolbachia
134(1)
7.3 Nerve Axons
135(2)
7.4 Calcium Handling
137(2)
Exercises
139(2)
Chapter 8 The Bistable Equation-Part II: Analysis 141(26)
8.1 Traveling Waves
141(5)
8.2 Threshold Behavior
146(4)
8.3 Propagation Failure
150(13)
Exercises
163(4)
Chapter 9 Advection and Reaction 167(40)
9.1 Simple Advection
167(1)
9.2 Advection with Decay
167(2)
9.3 Structured Populations
169(8)
9.4 Simulation
177(4)
9.5 Nonlinear Advection; Burgers' Equation
181(8)
9.6 Extras: More Advection-Reaction Models
189(11)
Exercises
200(7)
Chapter 10 Advection with Diffusion 207(10)
10.1 A Biased Random Walk
207(1)
10.2 Transport with Switching
207(2)
10.3 Ornstein-Uhlenbeck Process
209(3)
10.4 Spread of an Ornstein-Uhlenbeck Epidemic
212(2)
Exercises
214(3)
Chapter 11 Chemotaxis 217(10)
11.1 Amoeba Aggregation
219(5)
Exercises
224(3)
Chapter 12 Spatial Patterns 227(20)
12.1 The Turing Mechanism
228(4)
12.2 Tiger Bush Stripes
232(6)
12.3 Cell Polarity
238(6)
Exercises
244(3)
Chapter 13 Dispersal-Renewal Theory 247(6)
13.1 Invasive Species
247(4)
Exercises
251(2)
Chapter 14 Collective Behavior 253(22)
14.1 Quorum Sensing
253(9)
14.2 Flocking Behavior
262(10)
Exercises
272(3)
Appendix A. Introduction to Matlab 275(10)
A1 A Matlab Primer
275(4)
A2 List of Available Matlab Codes
279(6)
Appendix B. Constants, Units, and Functions 285(4)
B1 Physical Constants
285(2)
B2 Functions Used in this Book
287(2)
Appendix C. Selected Answers to Exercises 289(10)
C1 Selected Answers for
Chapter 1
289(2)
C2 Selected Answers for
Chapter 2
291(1)
C3 Selected Answers for
Chapter 3
291(1)
C4 Selected Answers for
Chapter 4
291(1)
C5 Selected Answers for
Chapter 5
292(1)
C6 Selected Answers for
Chapter 6
293(1)
C7 Selected Answers for
Chapter 7
293(1)
C8 Selected Answers for
Chapter 8
294(1)
C9 Selected Answers for
Chapter 9
295(1)
C10 Selected Answers for
Chapter 10
296(1)
C11 Selected Answers for
Chapter 11
297(1)
C12 Selected Answers for
Chapter 12
297(1)
C13 Selected Answers for
Chapter 13
297(1)
C14 Selected Answers for
Chapter 14
297(2)
Bibliography 299(6)
Index 305
James P. Keener, University of Utah, Salt Lake City, UT