Mathematics for neuroscientists
Virtually 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;...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
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Amsterdam ; Boston :
Elsevier
2010.
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| Edición: | 1st ed |
| Colección: | Elsevier science & technology books
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009797957606719 |
Tabla de Contenidos:
- Front 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
- 3.5. 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
- Chapter 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
- 8.3. 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
- 10.5. 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
- 12.1. Basic Synaptic Structure and Physiology
