Skip to main content
  • Textbook
  • © 2021

Mathematics as a Laboratory Tool

Dynamics, Delays and Noise

  • 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

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 64.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxv
  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

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

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 64.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access