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Calculus for cognitive scientists = partial differential equation models /

Record Type:	Language materials, printed : 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.;
Contained By:	Springer eBooks
Subject:	Calculus. -
Online resource:	http://dx.doi.org/10.1007/978-981-287-880-9
ISBN:	9789812878809

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

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

672391
Calculus.

LC Class. No.: QA303.2

Dewey Class. No.: 515

Calculus for cognitive scientists = partial differential equation models /
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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.
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