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© 2017

An Introduction to Modeling Neuronal Dynamics

Textbook

Part of the Texts in Applied Mathematics book series (TAM, volume 66)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Christoph Börgers
    Pages 1-8
  3. Modeling a Single Neuron

    1. Front Matter
      Pages 9-9
    2. Christoph Börgers
      Pages 11-14
    3. Christoph Börgers
      Pages 15-21
    4. Christoph Börgers
      Pages 23-29
    5. Christoph Börgers
      Pages 31-37
    6. Christoph Börgers
      Pages 39-43
    7. Christoph Börgers
      Pages 45-50
    8. Christoph Börgers
      Pages 57-69
  4. Dynamics of Single Neuron Models

    1. Front Matter
      Pages 71-71
    2. Christoph Börgers
      Pages 73-77
    3. Christoph Börgers
      Pages 79-84
    4. Christoph Börgers
      Pages 85-89
    5. Christoph Börgers
      Pages 91-97
    6. Christoph Börgers
      Pages 99-103
    7. Christoph Börgers
      Pages 105-110
    8. Christoph Börgers
      Pages 111-118
    9. Christoph Börgers
      Pages 119-129

About this book

Introduction

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology.

Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity.

An extensive online collection of Matlab programs generating the figures accompanies the book.  

Keywords

Single Neuron Models Mathematical Modeling Computational Neuroscience Hodgkin-Huxley Equations Differential Equations Brain Rhythms Synchronization Dynamics

Authors and affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA

About the authors

Christoph Börgers is Professor of Mathematics at Tufts University, USA.  His expertise is in mathematical neuroscience, applied dynamical systems, numerical analysis, and scientific computing. 

Bibliographic information

Reviews

“I would be happy to recommend this textbook to instructors seeking a textbook for an introductory course in mathematical neuroscience, and for students with quantitative backgrounds interested in taking such a course. … For those students beginning their climb from the established foundations of mathematical neuroscience towards these newer branches, An Introduction to Modeling Neuronal Dynamics offers a fine place to start.” (Braden A. W. Brinkman, SIAM Review, Vol. 61 (2), 2019)

“The book is supplemented with a helpful library of Matlab scripts that generate many of the plots and numerical results presented in it. The exercises encourage the readers to modify the scripts to create new plots ... the book takes the reader on a fascinating journey of neuronal dynamics via introduction, analysis and numerical simulation of relevant dynamical systems. It is written with clarity and rigor.” (Oksana Bihun, zbMATH 1382.92001, 2018)