Calculus for Cognitive Scientists

Partial Differential Equation Models

By:

James Peterson

Format:

Paperback / softback

Series:

Cognitive Science and Technology

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Description

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.

Author Biography:

Dr. James Peterson is an Associate Professor in Mathematical Sciences and Biological Sciences at Clemson University, USA. His formal training is in mathematics but he has worked as an aerospace engineer and a software engineer also. He enjoys working on very hard problems that require multiple disciplines to make sense out of and he reads, studies and plays in cutting edge areas a lot as part of his interests.

Release date NZ

December 9th, 2018

Author

James Peterson

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 2016

Illustrations

156 Illustrations, color; XXXI, 534 p. 156 illus. in color.

Pages

534

Series

Cognitive Science and Technology

ISBN-13

9789811357213

Product ID

28998406

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