Mathematical Foundations Of Neuroscience
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Mathematical Foundations Of Neuroscience
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Author : G. Bard Ermentrout
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-01
Mathematical Foundations Of Neuroscience written by G. Bard Ermentrout and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
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 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.
Mathematical Foundations Of Neuroscience
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Author : G. Bard Ermentrout
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-08
Mathematical Foundations Of Neuroscience written by G. Bard Ermentrout and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-08 with Mathematics categories.
Arising from several courses taught by the authors, this book provides a needed overview illustrating how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.
From Computer To Brain
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Author : William W. Lytton
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
From Computer To Brain written by William W. Lytton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Mathematics categories.
Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.
Mathematics For Neuroscientists
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Author : Fabrizio Gabbiani
language : en
Publisher: Academic Press
Release Date : 2017-02-04
Mathematics For Neuroscientists written by Fabrizio Gabbiani and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-04 with Mathematics categories.
Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. - Fully revised material and corrected text - Additional chapters on extracellular potentials, motion detection and neurovascular coupling - Revised selection of exercises with solutions - More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts
Spikes Decisions And Actions
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Author : Hugh Reid Wilson
language : en
Publisher:
Release Date : 1999
Spikes Decisions And Actions written by Hugh Reid Wilson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Medical categories.
The nervous system of higher animals is very complex and highly nonlinear. among its many capabilities are making decisions and carrying out complex motor actions such as swimming. Nonlinear dynamical modelling can be used to understand and explain neural phenomena at many different levels, including - ion-currents and action potentials; short - and long - term memory; visual hallucinations; neural synchronization; motor control This book explores the mathematical principles by which brains generate spikes, make decisions, store memories, and control actions. It assumes a basic knowledge of calculus and develops the dynamical foundations of neuroscience using problem sets and computer simulations on the accompanying PC and Mac compatible MatLab disk.
An Introduction To Modeling Neuronal Dynamics
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Author : Christoph Börgers
language : en
Publisher: Springer
Release Date : 2017-04-17
An Introduction To Modeling Neuronal Dynamics written by Christoph Börgers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-17 with Mathematics categories.
This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.
Foundations Of Cellular Neurophysiology
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Author : Daniel Johnston
language : en
Publisher: MIT Press
Release Date : 1994-11-02
Foundations Of Cellular Neurophysiology written by Daniel Johnston and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-02 with Medical categories.
with simulations and illustrations by Richard Gray Problem solving is an indispensable part of learning a quantitative science such as neurophysiology. This text for graduate and advanced undergraduate students in neuroscience, physiology, biophysics, and computational neuroscience provides comprehensive, mathematically sophisticated descriptions of modern principles of cellular neurophysiology. It is the only neurophysiology text that gives detailed derivations of equations, worked examples, and homework problem sets (with complete answers). Developed from notes for the course that the authors have taught since 1983, Foundations of Cellular Neurophysiology covers cellular neurophysiology (also some material at the molecular and systems levels) from its physical and mathematical foundations in a way that is far more rigorous than other commonly used texts in this area.
Space Time And Number In The Brain
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Author : Elizabeth Brannon
language : en
Publisher: Academic Press
Release Date : 2011-05-31
Space Time And Number In The Brain written by Elizabeth Brannon and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-31 with Mathematics categories.
The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields
Fundamentals Of Computational Neuroscience
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Author : Thomas Trappenberg
language : en
Publisher: Oxford University Press (UK)
Release Date : 2010
Fundamentals Of Computational Neuroscience written by Thomas Trappenberg and has been published by Oxford University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. It introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain. The book covers the introduction and motivation of simplified models of neurons that are suitable for exploring information processing in large brain-like networks. Additionally, it introduces several fundamental networkarchitectures and discusses their relevance for information processing in the brain, giving some examples of models of higher-order cognitive functions to demonstrate the advanced insight that can begained with such studies.
Foundations Of Mathematical Economics
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Author : Michael Carter
language : en
Publisher: MIT Press
Release Date : 2001-10-26
Foundations Of Mathematical Economics written by Michael Carter and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-26 with Business & Economics categories.
This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist.