Toru Ohira: Mathematics as a Laboratory Tool

Cover: 9783030695781 | Mathematics as a Laboratory Tool | Dynamics, Delays and Noise | Buch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

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

Inhaltsverzeichnis

Science and the Mathematics of Black Boxes.- The Mathematics of Change.- Equilibria and Steady States.- Stability.- Fixed Points: Creation and Destruction.- Transient Dynamics.- Frequency Domain I: Bode Plots and Transfer Functions.- Frequency Doman II: Fourier Analysis and Power Spectra.- Feedback and Control Systems-. Time delays.- Oscillations.- Characterizing and Manipulating Oscillations.- Beyond Limit Cycles.- Random Perturbations.- Noisy Dynamical Systems.- Random Walks.- Thermodynamic Perspectives.- Concluding Remarks.

Details

Erscheinungsjahr:	2021
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xxv 638 S. 202 s/w Illustr. 8 farbige Illustr. 638 p. 210 illus. 8 illus. in color.
ISBN-13:	9783030695781
ISBN-10:	3030695786
Sprache:	Englisch
Einband:	Gebunden
Autor:	Ohira, Toru Milton, John
Auflage:	Second Edition 2021
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 39 mm
Von/Mit:	Toru Ohira (u. a.)
Erscheinungsdatum:	12.08.2021
Gewicht:	1,271 kg