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Calculus for Cognitive Scientists: Partial Differential Equation Models (Cognitive Science and Technology) - Hardcover

Peterson, James

 
9789812878786: Calculus for Cognitive Scientists: Partial Differential Equation Models (Cognitive Science and Technology)
Hardcover
ISBN 10: 9812878785 ISBN 13: 9789812878786
Verlag: Springer, 2016

Inhaltsangabe

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics.  A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

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Über die Autorin bzw. den Autor

Dr. James Peterson is an Associate Professor in Mathematical Sciences and Biological Sciences at Clemson University, USA. His formal training is in mathematics but he has worked as an aerospace engineer and a software engineer also. He enjoys working on very hard problems that require multiple disciplines to make sense out of and he reads, studies and plays in cutting edge areas a lot as part of his interests.

Von der hinteren Coverseite

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

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Verlag
Springer
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
9812878785
ISBN 13 
9789812878786
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
565
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Deutschland

Weitere beliebte Ausgaben desselben Titels

9789811357213: Calculus for Cognitive Scientists: Partial Differential Equation Models (Cognitive Science and Technology)

Vorgestellte Ausgabe

ISBN 10:  9811357218 ISBN 13:  9789811357213
Verlag: Springer, 2018
Softcover