Stochastic analysis tackles randomness in physical systems by blending simulation methods with hands-on problem-solving strategies. It examines key concepts like Markov chains, Gaussian processes, Ito calculus and stochastic differential equations,...Lasīt vairāk
Mathematical ideas unite Statistical Mechanics and Conformal Field Theory by charting a path from two-dimensional lattice models and phase transitions to the emergence of 2D CFT, focusing on Unitary Minimal Models. Scaling assumptions and probabilis...Lasīt vairāk
Harmonic analysis is the study of functions by decomposing them into components that are special functions, says Varadhan, and he considers here only those aspects of the vast field that were part of the course he taught at the Courant Institute...Lasīt vairāk
This two-volume set focuses on linear algebra for graduate students in mathematics, the sciences, and economics. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in whi...Lasīt vairāk
In the second of two volumes for a one-year graduate course sequence in linear algebra, Greenleaf and Marques discuss more advanced topics in generalized eigenspaces and the Jordan decomposition; further applications of the Jordan form; and bilin...Lasīt vairāk
The first of two volumes on linear algebra for graduate students and advanced undergraduates, this book explains the structure of linear operators as the key to solving problems in which they arise. It describes basic ideas of linear algebra, inc...Lasīt vairāk
Erdos and Yau present a concise and self-contained introduction to recent techniques to prove local spectral universality for large random matrices. They focus mainly on the methods they participated in developing during the past few years, prese...Lasīt vairāk
Like the 2012 graduate course on which it is based, the book considers three sets of examples of large deviations in mathematics. One is diffusions with small noise and the exit problem. Another is the large time behavior of Markov processes and...Lasīt vairāk
In lecture notes from a graduate course at the Courant Institute of Mathematical Sciences, Percus and Childress describe mathematical models that can be used to understand the development of multi-celled animals from an initial single cell egg. Of pa...Lasīt vairāk
Friedrichs (1901-83) deals with electromagnetic theory from a mathematical perspective, which he says may be very different from the approach that a physicist or electrical engineer might take. He covers electrostatics, currents and Ohms law, magnet...Lasīt vairāk
Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a con...Lasīt vairāk
Percus (Courant Institute of Mathematical Sciences, New York U.) offers this book for mathematicians based on lecture notes from a course he has given on mathematical methods in immunology, focusing on the battle between the HIV virus and the adaptiv...Lasīt vairāk
Hoppensteadt taught the lecture course in computational biology and applied mathematics at the Courant Institute of Mathematical Sciences in the fall of 2010. The notes partly build on Modeling and Simulation in Medicine and the Life Sciences (2002)...Lasīt vairāk
Lin taught a course at the Courant Institute, New York University, in 1992, and in 1995 Han used and augmented the notes for a course at the University of Notre Dame. They present some basic methods for obtaining various a priori estimates for second...Lasīt vairāk
Researchers have spread out along three basic routes to the mathematical modeling of the very tiny moving parts in micro-electro-mechanical systems (MEMS), and it is the electrostatic (rather than thermal or biological) approach that Esposito (U. deg...Lasīt vairāk
This book is based on a course on advanced topics in differential equations given in Spring 2010 at the Courant Institute of Mathematical Sciences. It describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the...Lasīt vairāk
Childress (Courant Institute) developed the material for a one-semester graduate course introducing classical fluid mechanics within the mathematics curriculum that replaced the previous two-semester introductory sequence by combining ideal and visco...Lasīt vairāk
The study is based on a graduate course by Deift at the Courant Institute in Fall 2005, and a modified version of it that Gioev taught at the University of Rochester in Spring 2007. They begin by presenting a unified treatment of the algebraic aspect...Lasīt vairāk
Based on a course entitled Wigner measures and semiclassical limits of nonlinear Schrodinger equations, this book applies the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quan...Lasīt vairāk
An introduction to stochastic processes studying certain elementary continuous-time processes. It includes a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a fini...Lasīt vairāk
