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Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods illustrated edition [Pehme köide]

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  • Formaat: Paperback / softback, 321 pages, kõrgus x laius x paksus: 251x172x17 mm, kaal: 583 g, Illustrations
  • Sari: Mathematical Modeling and Computation No. 12
  • Ilmumisaeg: 30-Jun-2006
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716128
  • ISBN-13: 9780898716122
Teised raamatud teemal:
Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods illustrated editionSuurem pilt
  • Formaat: Paperback / softback, 321 pages, kõrgus x laius x paksus: 251x172x17 mm, kaal: 583 g, Illustrations
  • Sari: Mathematical Modeling and Computation No. 12
  • Ilmumisaeg: 30-Jun-2006
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716128
  • ISBN-13: 9780898716122
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780898716122.html
Märksõnad:
The field of mathematical biology is growing rapidly. Questions about infectious diseases, heart attacks, cell signaling, cell movement, ecology, environmental changes, and genomics are now being analyzed using mathematical and computational methods. A Course in Mathematical Biology teaches all aspects of modern mathematical modeling and is specifically designed to introduce undergraduate students to problem solving in the context of biology.

Divided into three parts, the book covers basic analytical modeling techniques and model validation methods; introduces computational tools used in the modeling of biological problems; and provides a source of open-ended problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, and there are many exercises related to biological questions. In addition, the book includes 25 open-ended research projects that can be used by students. The book is accompanied by a Web site that contains solutions to most of the exercises and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB®.

Arvustused

'There really is not a book that is directly comparable. Students will be able to study any area of biology with a mathematical perspective. The projects and the introduction to computation are a real bonus.' Fred Brauer, University of British Columbia 'One can warmly recommend this book to any undergraduate students in life science or mathematics who want to be introduced to the fascinating field of biomathematics.' J.-P. Gabriel, Département de Mathématiques de l'université, Fribourg

Muu info

This is the only book that teaches all aspects of modern mathematical modeling.
Preface ix
I Theoretical Modeling Tools
1(198)
Introduction
3(6)
The Modeling Process
3(1)
Probabilities and Rates
4(3)
Model Classes
7(1)
Exercises for Modeling
8(1)
Discrete-Time Models
9(46)
Introduction to Discrete-Time Models
9(1)
Scalar Discrete-Time Models
10(26)
Growth of a Population and the Discrete Logistic Equation
10(5)
Cobwebbing, Fixed Points, and Linear Stability Analysis
15(3)
Analysis of the Discrete Logistic Equation
18(7)
Alternatives to the Discrete Logistic Equation
25(4)
Models in Population Genetics
29(7)
Systems of Discrete-Time Equations
36(12)
Love Affairs: Introduction
36(2)
Fixed Points and Linear Stability Analysis for Systems of Discrete-Time Equations
38(4)
Love Affairs: Model Analysis
42(2)
Host-Parasitoid Models
44(4)
Exercises for Discrete-Time Models
48(7)
Ordinary Differential Equations
55(42)
Introduction to ODEs
55(1)
Scalar Equations
56(4)
The Picard-Lindelof Theorem
59(1)
Systems of Equations
60(6)
Reaction Kinetics
60(2)
A General Interaction Model for Two Populations
62(2)
A Basic Epidemic Model
64(1)
Nondimensionalization
65(1)
Qualitative Analysis of 2 x 2 Systems
66(14)
Phase-Plane Analysis: Linear Systems
67(7)
Nonlinear Systems and Linearization
74(2)
Qualitative Analysis of the General Population Interaction Model
76(2)
Qualitative Analysis of the Epidemic Model
78(2)
General Systems of Three or More Equations
80(1)
Discrete-Time Models from Continuous-Time Models
81(2)
Numerical Methods
81(1)
The Time-One Map
81(2)
Elementary Bifurcations
83(6)
Saddle-Node Bifurcation
84(1)
Transcritical Bifurcation
84(1)
Pitchfork Bifurcation
85(1)
Hopf Bifurcation
86(2)
The Spruce Budworm Model
88(1)
Further Reading
89(1)
Exercises for ODEs
90(7)
Partial Differential Equations
97(24)
Partial Derivatives
97(1)
An Age-Structured Model
98(4)
Derivation
98(2)
Solution
100(2)
Reaction-Diffusion Equations
102(13)
Derivation of Reaction-Diffusion Equations
102(2)
The Fundamental Solution
104(2)
Critical Domain Size
106(5)
Traveling Waves
111(4)
Further Reading
115(1)
Exercises for PDEs
116(5)
Stochastic Models
121(34)
Introduction
121(1)
Markov Chains
122(4)
A Two-Tree Forest Ecosystem
122(2)
Markov Chain Theory
124(1)
The Princeton Forest Ecosystem
124(2)
Working with Random Variables
126(6)
Probability Density
126(1)
Probability Mass
127(2)
Descriptive Statistics
129(1)
The Generating Function
130(2)
Diffusion Processes
132(4)
Random Motion in One Dimension
133(2)
Diffusion Equation
135(1)
Branching Processes
136(5)
Galton--Watson Process
136(3)
Polymerase Chain Reaction
139(2)
Linear Birth and Death Process
141(6)
Pure Birth Process
141(3)
Birth and Death Process
144(3)
Nonlinear Birth-Death Process
147(4)
A Model for the Common Cold in Households
148(1)
Embedded Time-Discrete Markov Process and Final Size Distribution
149(2)
Exercises for Stochastic Models
151(4)
Cellular Automata and Related Models
155(20)
Introduction to Cellular Automata
155(6)
Wolfram's Classification
157(2)
The Game of Life
159(1)
Some Theoretical Results on Cellular Automata
160(1)
Greenberg-Hastings Automata
161(4)
Relation to an SIR Model
164(1)
Generalized Cellular Automata
165(5)
Automata with Stochastic Rules
165(2)
Grid Modifications
167(1)
Asynchronous Dynamics
168(2)
Related Models
170(1)
Further Reading
171(1)
Exercises for Cellular Automata
172(3)
Estimating Parameters
175(24)
Introduction
175(1)
The Likelihood Function
176(11)
Stochastic Models without Measurement Error
176(5)
Deterministic Models
181(6)
Model Comparison
187(6)
Akaike Information Criterion
187(2)
Likelihood Ratio Test for Nested Models
189(3)
Cross Validation
192(1)
Optimization Algorithms
193(2)
Algorithms
193(1)
Positivity
194(1)
What Did We Learn?
195(1)
Further Reading
196(1)
Exercises for Parameter Estimation
196(3)
II Self-Guided Computer Tutorial
199(38)
Maple Course
201(36)
First Steps in Maple
201(11)
Constants and Functions
201(4)
Working with Data Sets
205(2)
Linear Regression
207(5)
Discrete Dynamical Systems: The Ricker Model
212(8)
Procedures in Maple
215(2)
Feigenbaum Diagram and Bifurcation Analysis
217(2)
Application of the Ricker Model to Vespula vulgaris
219(1)
Stochastic Models with Maple
220(3)
ODEs: Applications to an Epidemic Model and a Predator--Prey Model
223(5)
The SIR Model of Kermack and McKendrick
223(2)
A Predator--Prey Model
225(3)
PDEs: An Age-Structured Model
228(4)
Stochastic Models: Common Colds in Households
232(5)
Application to Data
234(3)
III Projects
237(46)
Project Descriptions
239(24)
Epidemic Models
239(6)
Population Dynamics
245(4)
Models for Spatial Spread
249(5)
Physiology
254(9)
Solved Projects
263(20)
Cell Competition
263(11)
Paramecium caudatum in Isolation
263(3)
The Two Populations in Competition
266(3)
Phase-Plane Analysis of the Competition Model
269(4)
Model Prediction
273(1)
An Alternative Hypothesis
273(1)
The Chemotactic Paradox
274(9)
A Resolution of the Chemotactic Paradox
274(4)
Discussion
278(5)
Appendix: Further Reading 283(4)
Bibliography 287(10)
Author Index 297(4)
Index 301