LEADER 05452nam 2200685 a 450 001 9910791474803321 005 20200520144314.0 010 $a1-282-76902-2 010 $a9786612769023 010 $a0-08-089049-0 035 $a(CKB)2560000000015252 035 $a(EBL)582009 035 $a(OCoLC)700688819 035 $a(SSID)ssj0000422821 035 $a(PQKBManifestationID)12156846 035 $a(PQKBTitleCode)TC0000422821 035 $a(PQKBWorkID)10432772 035 $a(PQKB)10287898 035 $a(MiAaPQ)EBC582009 035 $a(Au-PeEL)EBL582009 035 $a(CaPaEBR)ebr10415281 035 $a(CaONFJC)MIL276902 035 $a(PPN)17024878X 035 $a(EXLCZ)992560000000015252 100 $a20101013d2010 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematics for neuroscientists$b[electronic resource] /$fFabrizio Gabbiani, Steven J. Cox 205 $a1st ed. 210 $aAmsterdam ;$aBoston $cElsevier$d2010 215 $a1 online resource (505 p.) 225 0 $aElsevier science & technology books 300 $aDescription based upon print version of record. 311 $a0-12-374882-8 320 $aIncludes bibliographical references (p. 473-482) and index. 327 $aFront cover; Mathematics for Neuroscientists; Copyright page; Full Contents; Preface; Chapter 1. Introduction; 1.1. How to Use This Book; 1.2. Brain Facts Brief; 1.3. Mathematical Preliminaries; 1.4. Units; 1.5. Sources; Chapter 2. The Passive Isopotential Cell; 2.1. Introduction; 2.2. The Nernst Potential; 2.3. Membrane Conductance; 2.4. Membrane Capacitance and Current Balance; 2.5. Synaptic Conductance; 2.6. Summary and Sources; 2.7. Exercises; Chapter 3. Differential Equations; 3.1. Exact Solution; 3.2. Moment Methods*; 3.3. The Laplace Transform*; 3.4. Numerical Methods 327 $a3.5. Synaptic Input 3.6. Summary and Sources; 3.7. Exercises; Chapter 4. The Active Isopotential Cell; 4.1. The Delayed Rectifier Potassium Channel; 4.2. The Sodium Channel; 4.3. The Hodgkin-Huxley Equations; 4.4. The Transient Potassium Channel*; 4.5. Summary and Sources; 4.6. Exercises; Chapter 5. The Quasi-Active Isopotential Cell; 5.1. The Quasi-Active Model; 5.2. Numerical Methods; 5.3. Exact Solution via Eigenvector Expansion; 5.4. A Persistent Sodium Current*; 5.5. A Nonspecific Cation Current that is Activated by Hyperpolarization*; 5.6. Summary and Sources; 5.7. Exercises 327 $aChapter 6. The Passive Cable 6.1. The Discrete Passive Cable Equation; 6.2. Exact Solution Via Eigenvector Expansion; 6.3. Numerical Methods; 6.4. The Passive Cable Equation; 6.5. Synaptic Input; 6.6. Summary and Sources; 6.7. Exercises; Chapter 7. Fourier Series and Transforms; 7.1. Fourier Series; 7.2. The Discrete Fourier Transform; 7.3. The Continuous Fourier Transform; 7.4. Reconciling the Discrete and Continuous Fourier Transforms; 7.5. Summary and Sources; 7.6. Exercises; Chapter 8. The Passive Dendritic Tree; 8.1. The Discrete Passive Tree; 8.2. Eigenvector Expansion 327 $a8.3. Numerical Methods 8.4. The Passive Dendrite Equation; 8.5. The Equivalent Cylinder*; 8.6. Branched Eigenfunctions*; 8.7. Summary and Sources; 8.8. Exercises; Chapter 9. The Active Dendritic Tree; 9.1. The Active Uniform Cable; 9.2. On the Interaction of Active Uniform Cables*; 9.3. The Active Nonuniform Cable; 9.4. The Quasi-Active Cable*; 9.5. The Active Dendritic Tree; 9.6. Summary and Sources; 9.7. Exercises; Chapter 10. Reduced Single Neuron Models; 10.1. The Leaky Integrate-and-Fire Neuron; 10.2. Bursting Neurons; 10.3. Simplified Models of Bursting Neurons; 10.4. Summary and Sources 327 $a10.5. Exercises Chapter 11. Probability and Random Variables; 11.1. Events and Random Variables; 11.2. Binomial Random Variables; 11.3. Poisson Random Variables; 11.4. Gaussian Random Variables; 11.5. Cumulative Distribution Functions; 11.6. Conditional Probabilities*; 11.7. Sum of Independent Random Variables*; 11.8. Transformation of Random Variables*; 11.9. Random Vectors*; 11.10. Exponential and Gamma Distributed Random Variables; 11.11. The Homogeneous Poisson Process; 11.12. Summary and Sources; 11.13. Exercises; Chapter 12. Synaptic Transmission and Quantal Release 327 $a12.1. Basic Synaptic Structure and Physiology 330 $aVirtually all scientific problems in neuroscience require mathematical analysis, and all neuroscientists are increasingly required to have a significant understanding of mathematical methods. There is currently no comprehensive, integrated introductory book on the use of mathematics in neuroscience; existing books either concentrate solely on theoretical modeling or discuss mathematical concepts for the treatment of very specific problems. This book fills this need by systematically introducing mathematical and computational tools in precisely the contexts that first established their important 606 $aMedicine$xMathematics 606 $aNeurosciences 615 0$aMedicine$xMathematics. 615 0$aNeurosciences. 676 $a612.8 676 $a612.80151 700 $aGabbiani$b Fabrizio$0858256 701 $aCox$b Steven J$057197 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910791474803321 996 $aMathematics for neuroscientists$93719218 997 $aUNINA