Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic Structure (Cambridge Studies in Mathematical Biology) Review

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(More customer reviews)Of all the introductory texts on electrophysiology, this one is by far the most mathematically literate.This is a two volume set.Volume 1 covers Nernst Plaank equilibrium equations, integrate and fire neurons,linear cable theory and the Rall model of dendrites.Volume 2 delves into the theory of the action potential - Hodgkin Huxley eqs and the various spinoffs, and some stochastic theory of spontaneous activity. This book was published in 1988, so it predates much of the more recent electrophysiological theory including the zoo of channels and current sources that have been more recently characterized, or the theory of recurrent networks, for example.Also, there are other books - Aidley's Physiology of Excitable Cells, or Kandel and Schwartz - that convey more sense of the underlying biology.But for a mathematically coherent treatment of the bedrock concepts in electrophysiology, nothing else comes close.

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Product Description:
The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron--an electrically active nerve cell--and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principle mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two some familiarity with differential equations and linear algebra is desirable.

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