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Mathematical Models in the Biosciences II [Pehme köide]

  • Formaat: Paperback / softback, 496 pages, kõrgus x laius: 235x156 mm, 250 b-w illus.
  • Ilmumisaeg: 23-Nov-2021
  • Kirjastus: Yale University Press
  • ISBN-10: 0300253699
  • ISBN-13: 9780300253696
Teised raamatud teemal:
Mathematical Models in the Biosciences IISuurem pilt
  • Formaat: Paperback / softback, 496 pages, kõrgus x laius: 235x156 mm, 250 b-w illus.
  • Ilmumisaeg: 23-Nov-2021
  • Kirjastus: Yale University Press
  • ISBN-10: 0300253699
  • ISBN-13: 9780300253696
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780300253696.html
Märksõnad:
Volume Two of an award-winning professor&;s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences

This is the second of a two-part series exploring essential concepts of calculus in the context of biological systems. Building on the essential ideas and theories of basic calculus taught in Mathematical Models in the Biosciences I, this book focuses on epidemiological models, mathematical foundations of virus and antiviral dynamics, ion channel models and cardiac arrhythmias, vector calculus and applications, and evolutionary models of disease. It also develops differential equations and stochastic models of many biomedical processes, as well as virus dynamics, the Clancy-Rudy model to determine the genetic basis of cardiac arrhythmias, and a sketch of some systems biology. Based on the author&;s calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students.

Volume Two of an award-winning professor&;s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences

Arvustused

Clear, enthusiastic, and communicating a love of maths, this is a useful, engaging and well-written text.Becca Asquith, Professor of Mathematical Immunology, Imperial College London

"This is a wonderful book, wise and witty. It would have taught me most of the math I needed for my career in research if I did all the problems."Stephen Stearns, author of The Evolution of Life Histories and Evolutionary Medicine

This well-written book covers multivariate calculus and dynamical systems within the context of the biological sciences, providing well-chosen, up-to-date biomedical examples. The Markov chain, along with its many interesting applications, is also introduced.Hongyu He, Professor of Mathematics, Louisiana State University  

Preface ix
Ways to use this book xiii
Acknowledgments xvii
Review of Volume I xxi
13 Higher-dimensional differential equations
1(86)
13.1 Eigenvalues in higher dimensions
1(6)
13.2 SIR calculations
7(10)
13.3 Michaelis-Menten kinetics
17(5)
13.4 Virus dynamics basics
22(15)
13.5 Immune response dynamics
37(8)
13.6 The Hodgkin-Huxley equations
45(9)
13.7 Chaos in predator-prey systems
54(9)
13.8 The Duffing equation and final state sensitivity
63(10)
13.9 Controlling chaos
73(14)
14 Stochastic models
87(48)
14.1 Markov chains
88(17)
14.2 The Perron-Frobenius theorem
105(9)
14.3 Structured populations
114(9)
14.4 Reproductive value and sensitivity analysis
123(12)
15 A tiny bit of genetics
135(44)
15.1 The Hardy-Weinberg law and selection equations
136(10)
15.2 Price's equation and multilevel selection
146(4)
15.3 Fitness landscapes
150(8)
15.4 The quasispecies equation
158(5)
15.5 Bioinformatics
163(4)
15.6 Some other topics
167(12)
16 Markov chains in biology
179(46)
16.1 Genetic drift
180(10)
16.2 Matrix differential equations
190(7)
16.3 Ion channel dynamics
197(9)
16.4 The Clancy-Rudy cardiac arrhythmia model
206(9)
16.5 Tumor suppressor genes
215(10)
17 Some vector calculus
225(79)
17.1 Gradient fields
226(5)
17.2 Line integrals
231(12)
17.3 Double integrals
243(7)
17.4 Green's theorem
250(6)
17.5 Interesting geometries
256(7)
17.6 Bendixson's criterion
263(3)
17.7 The index of a fixed point
266(11)
17.8 Surface integrals
277(8)
17.9 Stokes' theorem
285(7)
17.10 Triple integrals
292(4)
17.11 Gauss' theorem
296(5)
17.12 Diffusion
301(3)
18 A glimpse of systems biology
304(25)
18.1 Genetic toggle switch
307(5)
18.2 Transcription networks
312(11)
18.3 Some other networks
323(5)
18.4 Why should this work?
328(1)
19 What's next?
329(24)
19.1 Evolutionary medicine
329(7)
19.2 Translational bioinformatics
336(5)
19.3 Topological methods
341(10)
19.4 No, really, what's next?
351(2)
Appendix A Technical Notes
353(63)
A.12 Some more linear algebra
353(9)
A.13 Some Markov chain properties
362(8)
A.14 Cell membrane channels
370(3)
A.15 Viruses and the immune system
373(16)
A.16 The normal density function
389(1)
A.17 A sketch of the Perron-Frobenius proof
390(3)
A.18 The Leslie matrix characteristic equation
393(2)
A.19 Liapunov exponents
395(3)
A.20 Stochastic resonance and the Duffing equation
398(4)
A.21 Proof of Lienard's theorem
402(4)
A.22 A bit of molecular genetics
406(10)
Appendix B Some Mathematica code
416(13)
B.11 Eigenvalues in higher dimensions
416(1)
B.12 SIR calculations
417(1)
B.13 Michaelis-Menten calculations
417(1)
B.14 Virus dynamics
417(1)
B.15 Immune system dynamics
418(1)
B.16 The Hodgkin-Huxley equations
419(2)
B.17 Chaos in predator-prey models
421(1)
B.18 The Duffing equation
421(1)
B.19 Control of chaos
422(2)
B.20 Sensitivity analysis
424(1)
B.21 The Clancy-Rudy model
424(1)
B.22 A genetic toggle switch
425(1)
B.23 Transcription networks
426(1)
B.24 Topological methods
426(3)
Appendix C Some useful integrals and hints 429(4)
References 433(20)
Index 453
Michael Frame retired in 2016 as adjunct professor of mathematics at Yale University. For more than twenty years Frame taught courses on fractal geometry and calculus based on applications in biology and medicine. Amelia Urry and he are the coauthors of Fractal Worlds: Grown, Built, and Imagined.