Mathematics as a laboratory tool: dynamics, delays and noise
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"...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2021]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Zusammenfassung: | 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 |
| Beschreibung: | 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 |
| Beschreibung: | xxv, 637 Seiten Illustrationen, Diagramme 235 mm |
| ISBN: | 9783030695781 |
Internformat
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Datensatz im Suchindex
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| edition | Second edition |
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| id | DE-604.BV047300653 |
| illustrated | Illustrated |
| index_date | 2024-07-03T17:23:21Z |
| indexdate | 2024-07-10T09:08:14Z |
| institution | BVB |
| isbn | 9783030695781 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032703821 |
| oclc_num | 1268178169 |
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| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xxv, 637 Seiten Illustrationen, Diagramme 235 mm |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Springer |
| record_format | marc |
| spelling | Milton, John Verfasser (DE-588)1060350475 aut Mathematics as a laboratory tool dynamics, delays and noise John Milton, Toru Ohira Second edition Cham, Switzerland Springer [2021] xxv, 637 Seiten Illustrationen, Diagramme 235 mm txt rdacontent n rdamedia nc rdacarrier 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 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 Biomathematics Neurology Cell physiology Mathematics Cytologie (DE-588)4070177-3 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Biologisches System (DE-588)4122930-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Biowissenschaftlerin (DE-588)4698137-8 gnd rswk-swf Neurologie (DE-588)4041888-1 gnd rswk-swf Hardcover, Softcover / Mathematik/Sonstiges Biologisches System (DE-588)4122930-7 s Neurologie (DE-588)4041888-1 s Biomathematik (DE-588)4139408-2 s DE-604 Mathematik (DE-588)4037944-9 s Cytologie (DE-588)4070177-3 s Biowissenschaftlerin (DE-588)4698137-8 s Ohira, Toru 1963- Verfasser (DE-588)1059084139 aut Erscheint auch als Online-Ausgabe 978-3-030-69579-8 Vorangegangen ist 978-1-4614-9095-1 |
| spellingShingle | Milton, John Ohira, Toru 1963- Mathematics as a laboratory tool dynamics, delays and noise Biomathematics Neurology Cell physiology Mathematics Cytologie (DE-588)4070177-3 gnd Biomathematik (DE-588)4139408-2 gnd Biologisches System (DE-588)4122930-7 gnd Mathematik (DE-588)4037944-9 gnd Biowissenschaftlerin (DE-588)4698137-8 gnd Neurologie (DE-588)4041888-1 gnd |
| subject_GND | (DE-588)4070177-3 (DE-588)4139408-2 (DE-588)4122930-7 (DE-588)4037944-9 (DE-588)4698137-8 (DE-588)4041888-1 |
| title | Mathematics as a laboratory tool dynamics, delays and noise |
| title_auth | Mathematics as a laboratory tool dynamics, delays and noise |
| title_exact_search | Mathematics as a laboratory tool dynamics, delays and noise |
| title_exact_search_txtP | Mathematics as a laboratory tool dynamics, delays and noise |
| title_full | Mathematics as a laboratory tool dynamics, delays and noise John Milton, Toru Ohira |
| title_fullStr | Mathematics as a laboratory tool dynamics, delays and noise John Milton, Toru Ohira |
| title_full_unstemmed | Mathematics as a laboratory tool dynamics, delays and noise John Milton, Toru Ohira |
| title_short | Mathematics as a laboratory tool |
| title_sort | mathematics as a laboratory tool dynamics delays and noise |
| title_sub | dynamics, delays and noise |
| topic | Biomathematics Neurology Cell physiology Mathematics Cytologie (DE-588)4070177-3 gnd Biomathematik (DE-588)4139408-2 gnd Biologisches System (DE-588)4122930-7 gnd Mathematik (DE-588)4037944-9 gnd Biowissenschaftlerin (DE-588)4698137-8 gnd Neurologie (DE-588)4041888-1 gnd |
| topic_facet | Biomathematics Neurology Cell physiology Mathematics Cytologie Biomathematik Biologisches System Mathematik Biowissenschaftlerin Neurologie |
| work_keys_str_mv | AT miltonjohn mathematicsasalaboratorytooldynamicsdelaysandnoise AT ohiratoru mathematicsasalaboratorytooldynamicsdelaysandnoise |