Calculus for Cognitive Scientists Partial Differential Equation Models
Başlık:
Calculus for Cognitive Scientists Partial Differential Equation Models
Yazar:
Peterson, James K. author.
ISBN:
9789812878809
Yazar:
Edisyon:
1st ed. 2016.
Fiziksel Niteleme:
XXXI, 534 p. 156 illus. in color. online resource.
Seri:
Cognitive Science and Technology,
İçindekiler:
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.
Özet:
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.
Konu Başlığı:
Ek Kurum Yazar:
Elektronik Erişim:
http://dx.doi.org/10.1007/978-981-287-880-9