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An Introduction to Modeling Neuronal Dynamics

  • Christoph Börgers

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
    10. Christoph Börgers
      Pages 131-140
    11. Christoph Börgers
      Pages 141-150
  5. Modeling Neuronal Communication

    1. Front Matter
      Pages 151-151
    2. Christoph Börgers
      Pages 153-164
    3. Christoph Börgers
      Pages 165-173
    4. Christoph Börgers
      Pages 175-180
  6. Entrainment, Synchronization, and Oscillations

    1. Front Matter
      Pages 181-181
    2. Christoph Börgers
      Pages 183-192
    3. Christoph Börgers
      Pages 193-197
    4. Christoph Börgers
      Pages 199-212
    5. Christoph Börgers
      Pages 213-226
    6. Christoph Börgers
      Pages 227-234
    7. Christoph Börgers
      Pages 235-242
    8. Christoph Börgers
      Pages 255-267
    9. Christoph Börgers
      Pages 269-280
    10. Christoph Börgers
      Pages 281-292
    11. Christoph Börgers
      Pages 293-300
    12. Christoph Börgers
      Pages 301-310
  7. Functional Significance of Synchrony and Oscillations

    1. Front Matter
      Pages 311-311
    2. Christoph Börgers
      Pages 313-321
    3. Christoph Börgers
      Pages 323-326
    4. Christoph Börgers
      Pages 327-332
    5. Christoph Börgers
      Pages 333-337
  8. Synaptic Plasticity

    1. Front Matter
      Pages 339-339
    2. Christoph Börgers
      Pages 341-348
    3. Christoph Börgers
      Pages 349-359
  9. Back Matter
    Pages 361-457

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

  • Christoph Börgers
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-51171-9
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-51170-2
  • Online ISBN 978-3-319-51171-9
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • Buy this book on publisher's site