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Mathematical foundations of neuroscience

Author: Bard Ermentrout; David H Terman
Publisher: New York : Springer, ©2010.
Series: Interdisciplinary applied mathematics, v. 35.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ermentrout, Bard.
Mathematical foundations of neuroscience.
New York : Springer, ©2010
(OCoLC)435421764
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Bard Ermentrout; David H Terman
ISBN: 9780387877082 0387877088 9780387877075 038787707X
OCLC Number: 663096613
Description: 1 online resource (xv, 422 pages) : illustrations (some color)
Contents: The Hodgkin-Huxley equations.-Dendrites --
Dynamics --
Voltage-gated channels --
Action potentials --
Synaptic channels --
Noise --
Networks --
Neuro oscillators --
Firing rate models --
Spatially distributed networks.
Series Title: Interdisciplinary applied mathematics, v. 35.
Responsibility: G. Bard Ermentrout, David H. Terman.
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Abstract:

This book applies methods from nonlinear dynamics to problems in neuroscience. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and  Read more...

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From the reviews:"This excellent 422 page hardcover publication is an accessible and concise monograph. ... Mathematical Foundations is a timely contribution that will prove useful to mathematics Read more...

 
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It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"The Hodgkin-Huxley equations.-Dendrites -- Dynamics -- Voltage-gated channels -- Action potentials -- Synaptic channels -- Noise -- Networks -- Neuro oscillators -- Firing rate models -- Spatially distributed networks.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/321713237<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Electronic books<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/321713237#Series\/interdisciplinary_applied_mathematics<\/a>> ; # Interdisciplinary applied mathematics ;<\/span>\n\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/worldcat.org\/issn\/0939-6047<\/a>> ; # Interdisciplinary applied mathematics,<\/span>\n\u00A0\u00A0\u00A0\nschema:isSimilarTo<\/a> <http:\/\/www.worldcat.org\/oclc\/435421764<\/a>> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Mathematical foundations of neuroscience<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"663096613<\/span>\" ;\u00A0\u00A0\u00A0\nschema:publication<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/663096613#PublicationEvent\/new_york_springer_2010<\/a>> ;\u00A0\u00A0\u00A0\nschema:publisher<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/321713237#Agent\/springer<\/a>> ; # Springer<\/span>\n\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/books.scholarsportal.info\/viewdoc.html?id=\/ebooks\/ebooks2\/springer\/2011-02-17\/1\/9780387877082<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/0-link-springer-com.pugwash.lib.warwick.ac.uk\/10.1007\/978-0-387-87708-2<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/link.springer.com\/openurl?genre=book&isbn=978-0-387-87707-5<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/catdir.loc.gov\/catdir\/enhancements\/fy1316\/2010929771-t.html<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/site.ebrary.com\/id\/10399992<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/doi.org\/10.1007\/978-0-387-87708-2<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/link.springer.com\/10.1007\/978-0-387-87708-2<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/link.springer.com\/openurl?genre=book&isbn=978-0-387-87707-5<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780387877082<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780387877075<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/663096613<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

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