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Calculus for cognitive scientists = ...

Peterson, James K.

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Calculus for cognitive scientists = partial differential equation models /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Calculus for cognitive scientists/ by James K. Peterson.
Reminder of title:	partial differential equation models /
Author:	Peterson, James K.
Published:	Singapore :Springer Singapore : : 2016.,
Description:	xxxi, 534 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Graham - Schmidt Orthogonalization -- Numerical Diﬀerential Equations -- Biological Molecules -- Ion Movement -- Lumped and Distributed Cell Models -- Time Independent Solutions to Inﬁnite Cables -- Time Independent Solutions to Finite and Half-Inﬁnite Space Cables -- A Primer On Series Solutions -- Linear Partial Diﬀerential Equations -- Simpliﬁed Dendrite - Soma - Axon Information Processing -- The Basic Hodgkin - Huxley Model -- Final Thoughts -- Background Reading.
Contained By:	Springer eBooks
Subject:	Calculus. -
Online resource:	http://dx.doi.org/10.1007/978-981-287-880-9
ISBN:	9789812878809$q(electronic bk.)

Calculus for cognitive scientists = partial differential equation models /
Peterson, James K.

Calculus for cognitive scientistspartial differential equation models /[electronic resource] :by James K. Peterson. - Singapore :Springer Singapore :2016. - xxxi, 534 p. :ill., digital ;24 cm. - Cognitive science and technology,2195-3988. - Cognitive science and technology..

Introduction -- Graham - Schmidt Orthogonalization -- Numerical Diﬀerential Equations -- Biological Molecules -- Ion Movement -- Lumped and Distributed Cell Models -- Time Independent Solutions to Inﬁnite Cables -- Time Independent Solutions to Finite and Half-Inﬁnite Space Cables -- A Primer On Series Solutions -- Linear Partial Diﬀerential Equations -- Simpliﬁed Dendrite - Soma - Axon Information Processing -- The Basic Hodgkin - Huxley Model -- Final Thoughts -- Background Reading.

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

ISBN: 9789812878809$q(electronic bk.)

Standard No.: 10.1007/978-981-287-880-9doiSubjects--Topical Terms:

517463
Calculus.

LC Class. No.: QA303.2

Dewey Class. No.: 515

Calculus for cognitive scientists = partial differential equation models /
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245 1 0 $a Calculus for cognitive scientists $h [electronic resource] : $b partial differential equation models / $c by James K. Peterson.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2016.
300 $a xxxi, 534 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cognitive science and technology, $x 2195-3988
505 0 $a Introduction -- Graham - Schmidt Orthogonalization -- Numerical Diﬀerential Equations -- Biological Molecules -- Ion Movement -- Lumped and Distributed Cell Models -- Time Independent Solutions to Inﬁnite Cables -- Time Independent Solutions to Finite and Half-Inﬁnite Space Cables -- A Primer On Series Solutions -- Linear Partial Diﬀerential Equations -- Simpliﬁed Dendrite - Soma - Axon Information Processing -- The Basic Hodgkin - Huxley Model -- Final Thoughts -- Background Reading.
520 $a This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.
650 0 $a Calculus. $3 517463
650 0 $a Differential equations, Partial. $3 518115
650 1 4 $a Engineering. $3 586835
650 2 4 $a Computational Intelligence. $3 1001631
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 1066859
650 2 4 $a Mathematical Models of Cognitive Processes and Neural Networks. $3 1619875
650 2 4 $a Artificial Intelligence (incl. Robotics) $3 890894
650 2 4 $a Computer Imaging, Vision, Pattern Recognition and Graphics. $3 890871
710 2 $a SpringerLink (Online service) $3 836513
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