Series:

Mathematical Analysis and Numerical Methods for Science

4 total works

Cover of Mathematical Analysis and Numerical Methods for Science and Technology
These 6 volumes -- the result of a 10 year collaboration between the authors, both distinguished international figures -- compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. The advent of high-speed computers has made it possible to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way.

Cover of Selected Papers II

Selected Papers II

by Peter Lax and Robert Dautray

Published 17 March 2011

A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields.

Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.

Cover of Dendritic Neurotransmitter Release
The transmission of the nervous impulse is always from the dendritic branches and the cell body to the axon or functional process. Every neuron, then, possesses a receptor apparatus, the body and the dendritic prolongations, an apparatus of emission, the axon, and the apparatus of distribution, the terminal arborization of the nerve fibers. I designated the foregoing principle: the theory of dynamic polarization (Cajal 1923). Ever since the beautiful drawings from Golgi and Cajal, we have been familiar with the organisation of neurones into dendritic, somatic and axonal compartments. Cajal proposed that these cellular compartments were specialised, resulting in his concept of ^dynamic polarisation'. He considered dendrites to be passive elements that simply transferred information from inputs to the soma. Since the discovery that dendrites of many neural populations release neuroactive substances and in doing so, alter neuronal output, it is now apparent that this theory requires qualification. This book presents recent developments in the neurophysiology of dendritic release of several chemical classes of transmitters in a number of different areas of the mammalian central nervous system. Once released from a neuron, these substances can act as neurotransmitters and/or neuromodulators, to autoregulate the original neuron, its synaptic inputs, and adjacent cells or, by volume transmission, to affect distant cells. In some systems, dendritic transmitter release is part independent of secretion from axon terminal signifying a selective control of the dendritic compartment.

Cover of Selected Papers I

A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields.

Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.