001438925 000__ 06587cam\a2200589\a\4500
001438925 001__ 1438925
001438925 003__ OCoLC
001438925 005__ 20230309004401.0
001438925 006__ m\\\\\o\\d\\\\\\\\
001438925 007__ cr\un\nnnunnun
001438925 008__ 210815s2021\\\\sz\\\\\\ob\\\\001\0\eng\d
001438925 019__ $$a1263873174$$a1273029741$$a1273420879
001438925 020__ $$a9783030695798$$q(electronic bk.)
001438925 020__ $$a3030695794$$q(electronic bk.)
001438925 020__ $$z3030695786
001438925 020__ $$z9783030695781
001438925 0247_ $$a10.1007/978-3-030-69579-8$$2doi
001438925 035__ $$aSP(OCoLC)1263985125
001438925 040__ $$aYDX$$beng$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCO$$dOCLCF$$dSFB$$dN$T$$dUKAHL$$dOCLCQ$$dCOM$$dOCLCO$$dOCLCQ
001438925 049__ $$aISEA
001438925 050_4 $$aQH323.5
001438925 08204 $$a570.1/51$$223
001438925 1001_ $$aMilton, John,$$d1950-
001438925 24510 $$aMathematics as a laboratory tool :$$bdynamics, delays and noise /$$cJohn Milton, Toru Ohira.
001438925 250__ $$aSecond edition.
001438925 260__ $$aCham, Switzerland :$$bSpringer,$$c2021.
001438925 300__ $$a1 online resource
001438925 336__ $$atext$$btxt$$2rdacontent
001438925 337__ $$acomputer$$bc$$2rdamedia
001438925 338__ $$aonline resource$$bcr$$2rdacarrier
001438925 504__ $$aIncludes bibliographical references and index.
001438925 5050_ $$aIntro -- 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
001438925 5058_ $$a2.1 Differentiation -- 2.2 Differential Equations -- 2.2.1 Population Growth -- 2.2.2 Time Scale of Change -- 2.2.3 Linear ODEs with Constant Coefficients -- 2.3 Black Boxes -- 2.3.1 Nonlinear Differential Equations -- 2.4 Existence and Uniqueness -- 2.5 What Have We Learned? -- 2.6 Exercises for Practice and Insight -- 3 Equilibria and Steady States -- 3.1 Law of Mass Action -- 3.2 Closed Dynamical Systems -- 3.2.1 Equilibria: Drug Binding -- 3.2.2 Transient Steady States: Enzyme Kinetics -- 3.3 Open Dynamical Systems -- 3.3.1 Water Fountains -- 3.4 The ``Steady-State Approximation''
001438925 5058_ $$a3.4.1 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
001438925 5058_ $$a4.4.2 Computer: Friend or Foe? -- 4.5 Cubic nonlinearity: excitable cells -- 4.5.1 The van der Pol Oscillator -- 4.5.2 Fitzhugh-Nagumo equation -- 4.6 Lyapunov's Insight -- 4.6.1 Conservative Dynamical Systems -- 4.6.2 Lyapunov's Direct Method -- 4.7 What Have We Learned? -- 4.8 Exercises for Practice and Insight -- 5 Fixed Points: Creation and Destruction -- 5.1 Saddle-Node Bifurcation -- 5.1.1 Neuron Bistability -- 5.2 Transcritical Bifurcation -- 5.2.1 Postponement of Instability -- 5.3 Pitchfork Bifurcation -- 5.3.1 Finger-Spring Compressions -- 5.4 Near the Bifurcation Point
001438925 5058_ $$a5.4.1 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
001438925 506__ $$aAccess limited to authorized users.
001438925 520__ $$aThe 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)
001438925 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed August 26, 2021).
001438925 650_0 $$aBiomathematics.
001438925 650_0 $$aDifferential equations.
001438925 650_6 $$aBiomathématiques.
001438925 650_6 $$aÉquations différentielles.
001438925 655_0 $$aElectronic books.
001438925 7001_ $$aOhira, Toru.
001438925 77608 $$iPrint version:$$aMilton, John, 1950-$$tMathematics as a laboratory tool.$$bSecond edition.$$dCham, Switzerland : Springer, 2021$$z3030695786$$z9783030695781$$w(OCoLC)1231958002
001438925 852__ $$bebk
001438925 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-69579-8$$zOnline Access$$91397441.1
001438925 909CO $$ooai:library.usi.edu:1438925$$pGLOBAL_SET
001438925 980__ $$aBIB
001438925 980__ $$aEBOOK
001438925 982__ $$aEbook
001438925 983__ $$aOnline
001438925 994__ $$a92$$bISE