| 书目名称 | Calculus for Cognitive Scientists |
| 副标题 | Partial Differential |
| 编辑 | James K. Peterson |
| 视频video | |
| 概述 | Derives the cable equation and the Hodgkin Huxley models for excitatory neurons from first principles of biophysics.Highlights theoretical and computational tools to enhance understanding of both the |
| 丛书名称 | Cognitive Science and Technology |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Book 2016 |
| 关键词 | Cable Equation; Graham-Schmidt Orthogonalization; Hodgkin - Huxley model; Ion movement; Lumped models; Ne |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-287-880-9 |
| isbn_softcover | 978-981-13-5721-3 |
| isbn_ebook | 978-981-287-880-9Series ISSN 2195-3988 Series E-ISSN 2195-3996 |
| issn_series | 2195-3988 |
| copyright | Springer Science+Business Media Singapore 2016 |
发表于 2025-3-21 17:09:16
