Calculus and mathematical analysis

This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis.

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations.

This book builds upon the revolutionary discovery made in 1974 that when one passes from function f to a function J of paths joining two points A1=A1 the connectivities R1 of the domain of f can be replaced by connectivities R1 over Q, common to the pathwise components of a basic Frechet space of classes of equivalent curves joining A1 to A1.

When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well.

The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers.

The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces.

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In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration.

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory.

Formal verification increasingly has become recognized as an answer to the problem of how to create ever more complex control systems, which nonetheless are required to behave reliably.

This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrodinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations.

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place.

This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems.

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian.

Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations.

Though the search for good selectors dates back to the early twentieth century, selectors play an increasingly important role in current research.

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces).

This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields.

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments.

The essential reference book on matrices-now fully updated and expanded, with new material on scalar and vector mathematicsSince its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics.

This book presents reverse mathematics to a general mathematical audience for the first time.

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Holder.

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view.

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "e;M"e; attached to a Shimura curve "e;M"e; over the field of rational numbers.

Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn).

An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals.

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group.

An essential introduction to the analysis and verification of control system softwareThe verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive.

How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to changeCalculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today.

This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime.

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics.

This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population.

This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M.

 For more than two thousand years, the Doubling of the Cube—the construction of the cube root of two using only a compass and straightedge—has stood as one of classical geometry's greatest impossibilities.

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today.

The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level.

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today.

Have you ever wondered why, despite their adorable exterior, rabbits haven't taken over the world?

A groundbreaking exploration of the laws governing the universe.

Esta obra es una exposición clara y completa de los nuevos programas de Matemáticas Especiales del primer ciclo universitario.

En la actualidad, la gestión de organizaciones requiere una precisión y eficacia cada vez mayores para enfrentar los desafíos cambiantes del mundo empresarial.

En esta obra se recogen los aspectos y metodos de analisis o calculo numerico lineal y no lineal esenciales para abordar muchos de los problemas de ingenieria aplicada basada en modelos matematicos, asi como las tecnicas mas extendidas de optimizacion lineal y discreta que complementan a los anteriores y en los que, en gran medida, se basan.

En este libro se hace una indagacion de corte historico-epistemologico de algunos desarrollos del analisis, la teoria de funciones y el analisis funcional en el siglo XIX y los inicios del siglo XX, cuando estas tres disciplinas se posesionan como ramas importantes de las matematicas.

Este es un manual basico y breve, de lectura asequible y en el que se desarrollan con concision, pero con el debido rigor y la necesaria claridad, los conocimientos basicos de la asignatura.

Este libro constituye el tercer volumen de la serie "Matemáticas para Ingeniería", que se centra en el cálculo diferencial e integral de funciones de varias variables, además del cálculo vectorial.

En este libro titulado "Matemáticas para Ingeniería II: Cálculo diferencial e integral", los autores entregan a sus lectores en 3 capítulos los conocimientos de cálculo diferencial y cálculo integral, los cuales son parte del eje de formación de ciencias de todos los planes de estudio de las carreras del área de ingeniería.

Las ecuaciones diferenciales nos permiten comprender la dinamica del mundo que nos rodea en nuestra vida cotidiana: desde el movimiento de los planetas en el espacio hasta el flujo de liquidos.