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Titlebook: Calculus for Cognitive Scientists; Partial Differential James K. Peterson Book 2016 Springer Science+Business Media Singapore 2016 Cable Eq

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https://doi.org/10.1007/978-1-4471-0951-8 looking at transient variables and the transient cable equation is derived. The transient cable equation then has a fundamental space and time constant associated with the membrane voltage solution which are important.
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Eliano Pessa,Maria Pietronilla Pennaand careful explanations of code choices. Finally, many sample action potential generation models are solved in the case of single and multiple applied pulses. The full dendritic cable model is then glued to the axon model to create a simple model of an excitatory cell.
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Ion Movementced. Then the Goldman–Hodgkin–Katz (GHK) equation is derived and used in multiple ion situations as well. We finish with a short description of excitable nerve cells and the generation of an action potential.
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The Basic Hodgkin–Huxley Modeland careful explanations of code choices. Finally, many sample action potential generation models are solved in the case of single and multiple applied pulses. The full dendritic cable model is then glued to the axon model to create a simple model of an excitatory cell.
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Simplified Dendrite—Soma—Axon Information Processing and leads of a family of separation constants that can only be obtained using root finding codes in MatLab. Such codes and their theoretical underpinnings are also discussed. The MatLab ball stick model code is then developed so that typical ball stick sample problems can be approximately solved.
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A Class of Cost Functions for IndependenceFourier cosine series. Then, all the tools are pulled together to find numerical approximations to a cable model with impulse current inputs. Finally, a careful explanation why the series solution solves the original cable model is presented.
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