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Mathematics as a Laboratory Tool

Dynamics, Delays and Noise

  • Textbook
  • © 2014

Overview

Authors:
  1. John Milton

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

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  2. Toru Ohira

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

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  • Uses mathematical methods that are used in the laboratory

  • Real laboratory exercises provided as supplementary material

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxv
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  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 57-90

  6. Fixed Points: Creation and Destruction

    • John Milton, Toru Ohira
    Pages 91-110

  7. Transient Dynamics

    • John Milton, Toru Ohira
    Pages 111-135

  8. Frequency Domain I: Bode Plots and Transfer Functions

    • John Milton, Toru Ohira
    Pages 137-173

  9. Frequency Domain II: Fourier Analysis and Power Spectra

    • John Milton, Toru Ohira
    Pages 175-218

  10. Feedback and Control Systems

    • John Milton, Toru Ohira
    Pages 219-257

  11. Oscillations

    • John Milton, Toru Ohira
    Pages 259-293

  12. Beyond Limit Cycles

    • John Milton, Toru Ohira
    Pages 295-319

  13. Random Perturbations

    • John Milton, Toru Ohira
    Pages 321-358

  14. Noisy Dynamical Systems

    • John Milton, Toru Ohira
    Pages 359-387

  15. Random Walks

    • John Milton, Toru Ohira
    Pages 389-424

  16. Thermodynamic Perspectives

    • John Milton, Toru Ohira
    Pages 425-457

  17. Concluding Remarks

    • John Milton, Toru Ohira
    Pages 459-460

  18. Back Matter

    Pages 461-500
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Keywords

About this book

This introductory textbook is based on the premise that the foundation of good science is good data. The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.

Reviews

“This book, written in an engaging and intuitive style, is aimed at undergraduate biology students; its primary goal is to provide a clear, comprehensive overview of the appropriate mathematical instruments for data collection and analysis, both deterministic and stochastic. … the book also has the stated goal of contributing to a better shaping of the curricula for undergraduate biology education towards a better coverage of analytic, mathematical and computational methods.” (Paul Georgescu, zbMATH 1319.92001, 2015)

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/10.1007/978-1-4614-9096-8

  • Publisher: Springer New York, NY

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

  • Copyright Information: Springer Science+Business Media New York 2014

  • Softcover ISBN: 978-1-4939-5254-0Published: 23 August 2016

  • eBook ISBN: 978-1-4614-9096-8Published: 18 September 2014

  • Edition Number: 1

  • Number of Pages: XXV, 500

  • Number of Illustrations: 158 b/w illustrations, 4 illustrations in colour

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

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