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Calculus for cognitive scientistspar...

Peterson, James K.

Calculus for cognitive scientistspartial differential equation models /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Calculus for cognitive scientistsby James K. Peterson.
其他題名:	partial differential equation models /
作者:	Peterson, James K.
出版者:	Singapore :Springer Singapore :2016.
面頁冊數:	xxxi, 534 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Calculus.
電子資源:	http://dx.doi.org/10.1007/978-981-287-880-9
ISBN:	9789812878809$q(electronic bk.)

Calculus for cognitive scientistspartial 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:

183091
Calculus.

LC Class. No.: QA303.2

Dewey Class. No.: 515

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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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