LEADER 03889nam 2200565 450 001 9910495183703321 005 20230619192656.0 010 $a3-030-69579-4 024 7 $a10.1007/978-3-030-69579-8 035 $a(CKB)4100000011996608 035 $a(DE-He213)978-3-030-69579-8 035 $a(MiAaPQ)EBC6698058 035 $a(Au-PeEL)EBL6698058 035 $a(OCoLC)1263873174 035 $a(PPN)257355243 035 $a(EXLCZ)994100000011996608 100 $a20220428d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematics as a laboratory tool $edynamics, delays and noise /$fJohn Milton, Toru Ohira 205 $aSecond edition. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (XXV, 638 p. 210 illus., 8 illus. in color.) 311 $a3-030-69578-6 320 $aIncludes bibliographical references and index. 327 $aScience 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. 330 $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). 606 $aBiomathematics 606 $aDifferential equations 606 $aBiomatemātica$2thub 606 $aEquacions diferencials$2thub 608 $aLlibres electrōnics$2thub 615 0$aBiomathematics. 615 0$aDifferential equations. 615 7$aBiomatemātica 615 7$aEquacions diferencials 676 $a570.151 700 $aMilton$b John$f1950-$01222521 702 $aOhira$b Toru 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910495183703321 996 $aMathematics as a laboratory tool$92835440 997 $aUNINA