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Biology in Time and Space: A Partial Differential Equation Modeling Approach

James P. Keener University of Utah, Salt Lake City, UT
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Softcover ISBN: 978-1-4704-5428-9
Product Code: AMSTEXT/50
List Price: $99.00 MAA Member Price:$89.10
AMS Member Price: $79.20 Electronic ISBN: 978-1-4704-6414-1 Product Code: AMSTEXT/50.E List Price:$99.00
MAA Member Price: $89.10 AMS Member Price:$79.20
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List Price: $148.50 MAA Member Price:$133.65
AMS Member Price: $118.80 Click above image for expanded view Biology in Time and Space: A Partial Differential Equation Modeling Approach James P. Keener University of Utah, Salt Lake City, UT Available Formats:  Softcover ISBN: 978-1-4704-5428-9 Product Code: AMSTEXT/50  List Price:$99.00 MAA Member Price: $89.10 AMS Member Price:$79.20
 Electronic ISBN: 978-1-4704-6414-1 Product Code: AMSTEXT/50.E
 List Price: $99.00 MAA Member Price:$89.10 AMS Member Price: $79.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$148.50 MAA Member Price: $133.65 AMS Member Price:$118.80
• Book Details

Volume: 502021; 308 pp
MSC: Primary 92; 35; Secondary 34; 60; 65;

How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.

The material is presented from a heavily computational perspective, using Matlab to compute solutions and to make plots. An appendix features a primer for Matlab and a list of Matlab codes used in the book, all of which are available for download here.

An instructor's solutions manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

Undergraduate and graduate students and researchers interested in mathematical biology and PDEs.

• Cover
• Title page
• Contents
• Preface
• Chapter 1. Background Material
• 1.1. Multivariable Calculus
• 1.2. Ordinary Differential Equations
• 1.3. Stochastic Processes
• Exercises
• Chapter 2. Conservation— Learning How to Count
• 2.1. The Conservation Law
• 2.2. Examples of Flux—How Things Move
• Exercises
• Chapter 3. The Diffusion Equation— Derivations
• 3.1. Discrete Boxes
• 3.2. A Random Walk
• 3.3. The Cable Equation
• Exercises
• Chapter 4. Realizations of a Diffusion Process
• 4.1. Following Individual Particles
• 4.2. Other Features of Brownian Particle Motion
• 4.3. Following Several Particles
• 4.4. Effective Diffusion
• 4.5. An Agent-Based Approach
• Exercises
• Chapter 5. Solutions of the Diffusion Equation
• 5.1. On an Infinite Domain
• 5.2. On the Semi-infinite Line
• 5.3. With Boundary Conditions
• 5.4. Separation of Variables
• 5.5. Numerical Methods
• 5.6. Comparison Theorems
• 5.7. FRAP
• Exercises
• Chapter 6. Diffusion and Reaction
• 6.1. Birth-Death with Diffusion
• 6.2. Growth with a Carrying Capacity—Fisher’s Equation
• 6.3. Resource Consumption
• 6.4. Spread of Rabies—SIR with Diffusion
• 6.5. Extras: Facilitated Diffusion
• Exercises
• Chapter 7. The Bistable Equation—Part I: Derivations
• 7.1. Spruce Budworm
• 7.2. Wolbachia
• 7.3. Nerve Axons
• 7.4. Calcium Handling
• Exercises
• Chapter 8. The Bistable Equation—Part II: Analysis
• 8.1. Traveling Waves
• 8.2. Threshold Behavior
• 8.3. Propagation Failure
• Exercises
• Chapter 9. Advection and Reaction
• 9.3. Structured Populations
• 9.4. Simulation
• 9.5. Nonlinear Advection; Burgers’ Equation
• 9.6. Extras: More Advection-Reaction Models
• Exercises
• Chapter 10. Advection with Diffusion
• 10.1. A Biased Random Walk
• 10.2. Transport with Switching
• 10.3. Ornstein–Uhlenbeck Process
• 10.4. Spread of an Ornstein–Uhlenbeck Epidemic
• Exercises
• Chapter 11. Chemotaxis
• 11.1. Amoeba Aggregation
• Exercises
• Chapter 12. Spatial Patterns
• 12.1. The Turing Mechanism
• 12.2. Tiger Bush Stripes
• 12.3. Cell Polarity
• Exercises
• Chapter 13. Dispersal-Renewal Theory
• 13.1. Invasive Species
• Exercises
• Chapter 14. Collective Behavior
• 14.1. Quorum Sensing
• 14.2. Flocking Behavior
• Exercises
• Appendix A. Introduction to Matlab
• A.1. A Matlab Primer
• A.2. List of Available Matlab Codes
• Appendix B. Constants, Units, and Functions
• B.1. Physical Constants
• B.2. Functions Used in this Book
• Appendix C. Selected Answers to Exercises
• C.1. Selected Answers for Chapter 1
• C.2. Selected Answers for Chapter 2
• C.3. Selected Answers for Chapter 3
• C.4. Selected Answers for Chapter 4
• C.5. Selected Answers for Chapter 5
• C.6. Selected Answers for Chapter 6
• C.7. Selected Answers for Chapter 7
• C.8. Selected Answers for Chapter 8
• C.9. Selected Answers for Chapter 9
• C.10. Selected Answers for Chapter 10
• C.11. Selected Answers for Chapter 11
• C.12. Selected Answers for Chapter 12
• C.13. Selected Answers for Chapter 13
• C.14. Selected Answers for Chapter 14
• Bibliography
• Index
• Back Cover

• Reviews

• "Biology in Time and Space" is an impressive introduction to spatial models of biological phenomena and their analysis. The book is a tour de force exploration of a huge variety of physical phenomena, mathematical models, as well as analytical and numerical tools for their analysis. As Michael Reed is quoted as saying on the back cover, this book is undoubtedly now one of the few foundational texts in Mathematical Biology.

Andrew Krause, Durham University
• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 502021; 308 pp
MSC: Primary 92; 35; Secondary 34; 60; 65;

How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.

The material is presented from a heavily computational perspective, using Matlab to compute solutions and to make plots. An appendix features a primer for Matlab and a list of Matlab codes used in the book, all of which are available for download here.

An instructor's solutions manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

Undergraduate and graduate students and researchers interested in mathematical biology and PDEs.

• Cover
• Title page
• Contents
• Preface
• Chapter 1. Background Material
• 1.1. Multivariable Calculus
• 1.2. Ordinary Differential Equations
• 1.3. Stochastic Processes
• Exercises
• Chapter 2. Conservation— Learning How to Count
• 2.1. The Conservation Law
• 2.2. Examples of Flux—How Things Move
• Exercises
• Chapter 3. The Diffusion Equation— Derivations
• 3.1. Discrete Boxes
• 3.2. A Random Walk
• 3.3. The Cable Equation
• Exercises
• Chapter 4. Realizations of a Diffusion Process
• 4.1. Following Individual Particles
• 4.2. Other Features of Brownian Particle Motion
• 4.3. Following Several Particles
• 4.4. Effective Diffusion
• 4.5. An Agent-Based Approach
• Exercises
• Chapter 5. Solutions of the Diffusion Equation
• 5.1. On an Infinite Domain
• 5.2. On the Semi-infinite Line
• 5.3. With Boundary Conditions
• 5.4. Separation of Variables
• 5.5. Numerical Methods
• 5.6. Comparison Theorems
• 5.7. FRAP
• Exercises
• Chapter 6. Diffusion and Reaction
• 6.1. Birth-Death with Diffusion
• 6.2. Growth with a Carrying Capacity—Fisher’s Equation
• 6.3. Resource Consumption
• 6.4. Spread of Rabies—SIR with Diffusion
• 6.5. Extras: Facilitated Diffusion
• Exercises
• Chapter 7. The Bistable Equation—Part I: Derivations
• 7.1. Spruce Budworm
• 7.2. Wolbachia
• 7.3. Nerve Axons
• 7.4. Calcium Handling
• Exercises
• Chapter 8. The Bistable Equation—Part II: Analysis
• 8.1. Traveling Waves
• 8.2. Threshold Behavior
• 8.3. Propagation Failure
• Exercises
• Chapter 9. Advection and Reaction
• 9.3. Structured Populations
• 9.4. Simulation
• 9.5. Nonlinear Advection; Burgers’ Equation
• 9.6. Extras: More Advection-Reaction Models
• Exercises
• Chapter 10. Advection with Diffusion
• 10.1. A Biased Random Walk
• 10.2. Transport with Switching
• 10.3. Ornstein–Uhlenbeck Process
• 10.4. Spread of an Ornstein–Uhlenbeck Epidemic
• Exercises
• Chapter 11. Chemotaxis
• 11.1. Amoeba Aggregation
• Exercises
• Chapter 12. Spatial Patterns
• 12.1. The Turing Mechanism
• 12.2. Tiger Bush Stripes
• 12.3. Cell Polarity
• Exercises
• Chapter 13. Dispersal-Renewal Theory
• 13.1. Invasive Species
• Exercises
• Chapter 14. Collective Behavior
• 14.1. Quorum Sensing
• 14.2. Flocking Behavior
• Exercises
• Appendix A. Introduction to Matlab
• A.1. A Matlab Primer
• A.2. List of Available Matlab Codes
• Appendix B. Constants, Units, and Functions
• B.1. Physical Constants
• B.2. Functions Used in this Book
• Appendix C. Selected Answers to Exercises
• C.1. Selected Answers for Chapter 1
• C.2. Selected Answers for Chapter 2
• C.3. Selected Answers for Chapter 3
• C.4. Selected Answers for Chapter 4
• C.5. Selected Answers for Chapter 5
• C.6. Selected Answers for Chapter 6
• C.7. Selected Answers for Chapter 7
• C.8. Selected Answers for Chapter 8
• C.9. Selected Answers for Chapter 9
• C.10. Selected Answers for Chapter 10
• C.11. Selected Answers for Chapter 11
• C.12. Selected Answers for Chapter 12
• C.13. Selected Answers for Chapter 13
• C.14. Selected Answers for Chapter 14
• Bibliography
• Index
• Back Cover
• "Biology in Time and Space" is an impressive introduction to spatial models of biological phenomena and their analysis. The book is a tour de force exploration of a huge variety of physical phenomena, mathematical models, as well as analytical and numerical tools for their analysis. As Michael Reed is quoted as saying on the back cover, this book is undoubtedly now one of the few foundational texts in Mathematical Biology.

Andrew Krause, Durham University
• 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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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