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Mathematics as a Laboratory Tool

Dynamics, Delays and Noise

  • Textbook
  • © 2021

Overview

Authors:
  1. John Milton

    1. W.M. Keck Science Department, The Claremont Colleges, Claremont, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Toru Ohira

    1. Graduate School of Mathematics, Nagoya University, Nagoya, Japan

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    You can also search for this author in PubMed   Google Scholar

  • Presents mathematical theory to non-mathematicians

  • Includes exercises and chapter-level Q&A

  • Applies laboratory methodology and incorporates real laboratory exercises as supplementary material

  • Progresses in concept complexity from introductory to advanced

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxv
    Download chapter PDF

  2. Science and the Mathematics of Black Boxes

    • John Milton, Toru Ohira
    Pages 1-15

  3. The Mathematics of Change

    • John Milton, Toru Ohira
    Pages 17-31

  4. Equilibria and Steady States

    • John Milton, Toru Ohira
    Pages 33-56

  5. Stability

    • John Milton, Toru Ohira
    Pages 57-93

  6. Fixed Points: Creation and Destruction

    • John Milton, Toru Ohira
    Pages 95-114

  7. Transient Dynamics

    • John Milton, Toru Ohira
    Pages 115-138

  8. Frequency Domain I: Bode Plots and Transfer Functions

    • John Milton, Toru Ohira
    Pages 139-175

  9. Frequency Domain II: Fourier Analysis and Power Spectra

    • John Milton, Toru Ohira
    Pages 177-219

  10. Feedback and Control Systems

    • John Milton, Toru Ohira
    Pages 221-251

  11. Time delays

    • John Milton, Toru Ohira
    Pages 253-302

  12. Oscillations

    • John Milton, Toru Ohira
    Pages 303-337

  13. Characterizing and Manipulating Oscillations

    • John Milton, Toru Ohira
    Pages 339-362

  14. Beyond Limit Cycles

    • John Milton, Toru Ohira
    Pages 363-394

  15. Random Perturbations

    • John Milton, Toru Ohira
    Pages 395-449

  16. Noisy Dynamical Systems

    • John Milton, Toru Ohira
    Pages 451-479

  17. Random Walks

    • John Milton, Toru Ohira
    Pages 481-533

  18. Thermodynamic Perspectives

    • John Milton, Toru Ohira
    Pages 535-567

  19. Concluding Remarks

    • John Milton, Toru Ohira
    Pages 569-570

  20. Back Matter

    Pages 571-638
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Keywords

About this book

The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students.  The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems.  The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology.   The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations.
 
Every effort has been made to ensure that the material is accessible to those with a background in calculus.  The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools.   Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.


Authors and Affiliations

  • W.M. Keck Science Department, The Claremont Colleges, Claremont, USA

    John Milton

  • Graduate School of Mathematics, Nagoya University, Nagoya, Japan

    Toru Ohira

About the authors

John Milton, Professor of Biology and William R. Kenan Jr Chair n Computational Neuroscience, The Claremont Colleges; Adjunct Professor of Biotechnology, Keck Graduate Institute 

Toru Ohira, Professor Mathematics, Graduate School of Mathematics, Nagoya University, Japan

Bibliographic Information

  • Book Title: Mathematics as a Laboratory Tool

  • Book Subtitle: Dynamics, Delays and Noise

  • Authors: John Milton, Toru Ohira

  • DOI: https://doi.org/10.1007/978-3-030-69579-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-69578-1Published: 12 August 2021

  • Softcover ISBN: 978-3-030-69581-1Published: 13 August 2022

  • eBook ISBN: 978-3-030-69579-8Published: 11 August 2021

  • Edition Number: 2

  • Number of Pages: XXV, 638

  • Number of Illustrations: 202 b/w illustrations, 8 illustrations in colour

  • Topics: Mathematical and Computational Biology, Neurology, Cell Physiology

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