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What every neuroscientist should know about the mathematical modeling of excitable cells. Combining empirical physiology and nonlinear dynamics, this text provides an introduction to the simulation and modeling of dynamic phenomena in cell biology and neuroscience. It introduces mathematical modeling techniques alongside cellular electrophysiology. Topics include membrane transport and diffusion, the biophysics of excitable membranes, the gating of voltage and ligand-gated ion channels, intracellular calcium signalling, and electrical bursting in neurons and other excitable cell types. It introduces mathematical modeling techniques such as ordinary differential equations, phase plane, and bifurcation analysis of single-compartment neuron models. With analytical and computational problem sets, this book is suitable for life sciences majors, in biology to neuroscience, with one year of calculus, as well as graduate students looking for a primer on membrane excitability and calcium signalling.
What every neuroscientist should know about the mathematical modeling of excitable cells, presented at an introductory level.
Providing a step-by-step and practical account of how to model neurons and neural circuitry, this textbook is designed for advanced undergraduate and postgraduate students of computational neuroscience as well as for researchers in neuroscience and related sciences wishing to apply computational approaches to interpret data and make predictions.
Learn to use computational modelling techniques to understand the nervous system at all levels, from ion channels to networks.
Erwin Schrödinger's book What is Life? had a tremendous influence on the development of molecular biology, stimulating scientists such as Watson and Crick to explore the physical basis of life. Much of the appeal of Schrödinger's book lay in its approach to the central problems in biology - heredity and how organisms use energy to maintain order - from a physicist's perspective. At Trinity College, Dublin a number of outstanding scientists from a range of disciplines gathered to celebrate the fiftieth anniversary of What is Life? and following Schrödinger's example fifty years previously, presented their views on the current central problems in biology. The contributors to this volume include Stephen Jay Gould, Roger Penrose, Jared Diamond, Manfred Eigen, John Maynard Smith, Christien de Duve and Lewis Wolpert. This collection is essential reading for anyone interested in biology and its future.
Covers all of the equations that candidates need to understand and be able to apply when sitting postgraduate anaesthetic examinations.
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation...
Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. While mastery of these equations is essential, adhering to any one method of solving them is not: this book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behaviour. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergradute, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations.
The 1994 IUCN Red List of Threatened Animals was a major advance on its predecessors in clarity of layout and amount of information presented. This is taken further in the 1996 edition, which is also the first global compilation to use the complete new IUCN Red List category system.