Presents an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. This book keeps the requirements of mathematical techniques minimal but gives detailed proofs and many examples and illustrations from p

Written by a leading specialist in the area of atmosphere/ocean science (AOS), these lecture notes present an introduction to this important topic. The goals of the lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied...

Presents an overview of the basic methods and concepts in mechanics of applied mathematics or related fields. This book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanic

This text is based on a course entitled 'Wigner measures and semiclassical limits of nonlinear Schrodinger equations'. The purpose of the book is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics."

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 finite numb

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book p

This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation.

Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out certain aspects of curves and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear and...

This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Supersymmetry has been studied by theoretical physicists since the early 1970s. This book presents a cogent and self-contained exposition of the foundations of supersymmetry for the mathematically-minded reader. It is suitable for graduate students and mathematicians interested in the mathematical theory of supersymmetry.