000 03472nam a22005535i 4500
001 978-981-287-880-9
003 DE-He213
005 20200420220215.0
007 cr nn 008mamaa
008 160211s2016 si | s |||| 0|eng d
020 _a9789812878809
_9978-981-287-880-9
024 7 _a10.1007/978-981-287-880-9
_2doi
050 4 _aQ342
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aPeterson, James K.
_eauthor.
245 1 0 _aCalculus for Cognitive Scientists
_h[electronic resource] :
_bPartial Differential Equation Models /
_cby James K. Peterson.
250 _a1st ed. 2016.
264 1 _aSingapore :
_bSpringer Singapore :
_bImprint: Springer,
_c2016.
300 _aXXXI, 534 p. 156 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aCognitive Science and Technology,
_x2195-3988
505 0 _aIntroduction -- Graham - Schmidt Orthogonalization -- Numerical Differential Equations -- Biological Molecules -- Ion Movement -- Lumped and Distributed Cell Models -- Time Independent Solutions to Infinite Cables -- Time Independent Solutions to Finite and Half-Infinite Space Cables -- A Primer On Series Solutions -- Linear Partial Differential Equations -- Simplified Dendrite - Soma - Axon Information Processing -- The Basic Hodgkin - Huxley Model -- Final Thoughts -- Background Reading.
520 _aThis 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.
650 0 _aEngineering.
650 0 _aArtificial intelligence.
650 0 _aComputer graphics.
650 0 _aNeural networks (Computer science).
650 0 _aPhysics.
650 0 _aComputational intelligence.
650 1 4 _aEngineering.
650 2 4 _aComputational Intelligence.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
650 2 4 _aMathematical Models of Cognitive Processes and Neural Networks.
650 2 4 _aArtificial Intelligence (incl. Robotics).
650 2 4 _aComputer Imaging, Vision, Pattern Recognition and Graphics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789812878786
830 0 _aCognitive Science and Technology,
_x2195-3988
856 4 0 _uhttp://dx.doi.org/10.1007/978-981-287-880-9
912 _aZDB-2-ENG
942 _cEBK
999 _c51526
_d51526