Texts in Applied Mathematics

An Introduction to Modeling Neuronal Dynamics

Authors: Börgers, Christoph

  • Includes access to Matlab codes generating the figuresExercises at widely varying levels are included at the end of every chapter
  • Detailed writing allows for self-study opportunities 
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Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-51171-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-3-319-51170-2
  • with online files
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.  

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. 

Reviews

“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)

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Table of contents (40 chapters)

  • Vocabulary and Notation

    Börgers, Christoph

    Pages 1-8

  • The Nernst Equilibrium

    Börgers, Christoph

    Pages 11-14

  • The Classical Hodgkin-Huxley ODEs

    Börgers, Christoph

    Pages 15-21

  • Numerical Solution of the Hodgkin-Huxley ODEs

    Börgers, Christoph

    Pages 23-29

  • Three Simple Models of Neurons in Rodent Brains

    Börgers, Christoph

    Pages 31-37

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-51171-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-3-319-51170-2
  • with online files
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Modeling Neuronal Dynamics
Authors
Series Title
Texts in Applied Mathematics
Series Volume
66
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-51171-9
DOI
10.1007/978-3-319-51171-9
Hardcover ISBN
978-3-319-51170-2
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XIII, 457
Number of Illustrations and Tables
170 b/w illustrations, 186 illustrations in colour
Topics