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210815s2021 sz ob 001 0 eng d |
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|a YDX
|b eng
|e pn
|c YDX
|d GW5XE
|d EBLCP
|d OCLCO
|d OCLCF
|d SFB
|d N$T
|d UKAHL
|d OCLCQ
|d COM
|d OCLCO
|d OCLCQ
|d OCLCO
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|d OCLCL
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| 019 |
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|a 1263873174
|a 1273029741
|a 1273420879
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|a 9783030695798
|q (electronic bk.)
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|a 3030695794
|q (electronic bk.)
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|z 3030695786
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|z 9783030695781
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|a 10.1007/978-3-030-69579-8
|2 doi
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| 035 |
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|a (OCoLC)1263985125
|z (OCoLC)1263873174
|z (OCoLC)1273029741
|z (OCoLC)1273420879
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|a QH323.5
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| 072 |
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|a MAT003000
|2 bisacsh
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|a PDE
|2 bicssc
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|a PDE
|2 thema
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|a HCDD
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| 100 |
1 |
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|a Milton, John,
|d 1950-
|1 https://id.oclc.org/worldcat/entity/E39PCjvPwgR676Mjpf9qXCHvjK
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| 245 |
1 |
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|a Mathematics as a laboratory tool :
|b dynamics, delays and noise /
|c John Milton, Toru Ohira.
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| 250 |
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|a Second edition.
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| 260 |
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|a Cham, Switzerland :
|b Springer,
|c 2021.
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| 300 |
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|a 1 online resource
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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0 |
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|a Intro -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgements for the Second Edition -- Contents -- Notation -- Tools -- 1 Science and the Mathematics of Black Boxes -- 1.1 The Scientific Method -- 1.2 Dynamical Systems -- 1.2.1 Variables -- 1.2.2 Measurements -- 1.2.3 Units -- 1.3 Input-Output Relationships -- 1.3.1 Linear Versus Nonlinear Black Boxes -- 1.3.2 The Neuron as a Dynamical System -- 1.4 Interactions Between System and Surroundings -- 1.5 What Have We Learned? -- 1.6 Exercises for Practice and Insight -- 2 The Mathematics of Change
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| 505 |
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|a 2.1 Differentiation -- 2.2 Differential Equations -- 2.2.1 Population Growth -- 2.2.2 Time Scale of Change -- 2.2.3 Linear ODEs with Constant Coefficients -- 2.3 Black Boxes -- 2.3.1 Nonlinear Differential Equations -- 2.4 Existence and Uniqueness -- 2.5 What Have We Learned? -- 2.6 Exercises for Practice and Insight -- 3 Equilibria and Steady States -- 3.1 Law of Mass Action -- 3.2 Closed Dynamical Systems -- 3.2.1 Equilibria: Drug Binding -- 3.2.2 Transient Steady States: Enzyme Kinetics -- 3.3 Open Dynamical Systems -- 3.3.1 Water Fountains -- 3.4 The ``Steady-State Approximation''
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|a 3.4.1 Steady State: Enzyme-Substrate Reactions -- 3.4.2 Steady State: Consecutive Reactions -- 3.5 Existence of Fixed Points -- 3.6 What Have We learned? -- 3.7 Exercises for Practice and Insight -- 4 Stability -- 4.1 Landscapes in Stability -- 4.1.1 Postural Stability -- 4.1.2 Perception of Ambiguous Figures -- 4.1.3 Stopping Epileptic Seizures -- 4.2 Fixed-Point Stability -- 4.3 Stability of Second-Order ODEs -- 4.3.1 Real Eigenvalues -- 4.3.2 Complex Eigenvalues -- 4.3.3 Phase-Plane Representation -- 4.4 Illustrative Examples -- 4.4.1 The Lotka-Volterra Equation
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|a 4.4.2 Computer: Friend or Foe? -- 4.5 Cubic nonlinearity: excitable cells -- 4.5.1 The van der Pol Oscillator -- 4.5.2 Fitzhugh-Nagumo equation -- 4.6 Lyapunov's Insight -- 4.6.1 Conservative Dynamical Systems -- 4.6.2 Lyapunov's Direct Method -- 4.7 What Have We Learned? -- 4.8 Exercises for Practice and Insight -- 5 Fixed Points: Creation and Destruction -- 5.1 Saddle-Node Bifurcation -- 5.1.1 Neuron Bistability -- 5.2 Transcritical Bifurcation -- 5.2.1 Postponement of Instability -- 5.3 Pitchfork Bifurcation -- 5.3.1 Finger-Spring Compressions -- 5.4 Near the Bifurcation Point
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|a 5.4.1 The Slowing-Down Phenomenon -- 5.4.2 Critical Phenomena -- 5.5 Bifurcations at the Benchtop -- 5.6 What Have We Learned? -- 5.7 Exercises for Practice and Insight -- 6 Transient Dynamics -- 6.1 Step Functions -- 6.2 Ramp Functions -- 6.3 Impulse Responses -- 6.3.1 Measuring the Impulse Response -- 6.4 The Convolution Integral -- 6.4.1 Summing Neuronal Inputs -- 6.5 Transients in Nonlinear Dynamical Systems -- 6.6 Neuron spiking thresholds -- 6.6.1 Bounded Time-Dependent States -- 6.7 What Have We Learned? -- 6.8 Exercises for Practice and Insight
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|a Includes bibliographical references and index.
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| 520 |
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|a 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. Review: "Based on the authors' experience teaching biology students, this book introduces a wide range of mathematical techniques in a lively and engaging style. Examples drawn from the authors' experimental and neurological studies provide a rich source of material for computer laboratories that solidify the concepts. The book will be an invaluable resource for biology students and scientists interested in practical applications of mathematics to analyze mechanisms of complex biological rhythms." (Leon Glass, McGill University, 2013)
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| 588 |
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|a Online resource; title from PDF title page (SpringerLink, viewed August 26, 2021).
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| 650 |
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|a Biomathematics.
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| 650 |
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|a Differential equations.
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| 650 |
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7 |
|a Ecuaciones diferenciales
|2 embne
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| 650 |
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7 |
|a Biomatemáticas
|2 embne
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| 650 |
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7 |
|a Biomathematics
|2 fast
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| 650 |
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7 |
|a Differential equations
|2 fast
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| 700 |
1 |
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|a Ohira, Toru.
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| 758 |
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|i has work:
|a Mathematics as a laboratory tool (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCG7wXxxPBFhQCvwh46yDbd
|4 https://id.oclc.org/worldcat/ontology/hasWork
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| 776 |
0 |
8 |
|i Print version:
|a Milton, John, 1950-
|t Mathematics as a laboratory tool.
|b Second edition.
|d Cham, Switzerland : Springer, 2021
|z 3030695786
|z 9783030695781
|w (OCoLC)1231958002
|
| 856 |
4 |
0 |
|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-030-69579-8
|y Click for online access
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| 903 |
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|a SPRING-MATH2021
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| 994 |
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|a 92
|b HCD
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