Differential calculus and equations

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.

A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis.

This book provides an introduction to the theory of dynamical systems with the (R) aid of the Mathematica computer algebra system.

The term convexity used to describe these lectures given at the Univer- sity of Lund in 1991-92 should be understood in a wide sense.

A new edition in a single volume Over the past decade, more and more sophisticaced mathematical tools and approaches have been incorporated in the ?

Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of these major types of system models: finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics.

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control.

In many problems arising in engineering and science one requires approxi- tion methods to reproduce physical reality as well as possible.

In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincare center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories).

The primary focus of this book is on explicating the direct method approach.

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena.

This is a revised and extended version of my 1995 elementary introduction to partial di?

More than ten years have passed since the book of F.

This little book is a revised and expanded version of one I wrote for the "e;VIII Latin American School of Mathematics"e; [29], in Portuguese, based on which I have periodically taught a topics course over the last 18 years.

This collection of original articles and surveys treats the linear and nonlinear aspects of the theory of partial differential equations.

One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system.

This volume is dedicated to John Benedetto.

One of the key issues related to superfluidity is the existence of vortices.

The study of CR manifolds lies at the intersection of three main mathematical disciplines, partial differential equations: complex analysis in several complex variables, and differential geometry.

This book traces the history of approximation theory from Leonhard Euler's cartographic investigations at the end of the 18th century to the early 20th century work of Sergei Bernstein defining a new branch of function theory.

Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology.

The problem of asymptotic regulation of the output of a dynamical system plays a central role in control theory.

The control and estimation of continuous-time/continuous-space nonlinear systems continues to be a challenging problem, and this is one of the c- tral foci of this book.

The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations.

This book gives an elementary introduction to a classical area of mathemat- ics - approximation theory - in a way that naturally leads to the modern field of wavelets.

Complex variables is a precise, elegant, and captivating subject.

Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition.

Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established.

Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established.

This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics.

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics.

"e;An exceptionally complete overview.

Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context.

This volume!

Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications.

The fascinating ?

This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions.

A self-contained text for an introductory course, this volume places strong emphasis on physical applications.

Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text.

Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathematical physics.

An almost entirely self-taught mathematical genius, George Green (1793 1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations.

This introductory treatment covers the basic concepts and machinery of stability theory.

Second volume of a highly regarded two-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order.

Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations.

This first volume of a highly regarded two-volume text is fully usable on its own.

Superb introduction devotes almost half its pages to numerical methods for solving partial differential equations, while the heart of the book focuses on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more.

This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems.

"e;Cartan's work provides a superb text for an undergraduate course in advanced calculus, but at the same time it furnishes the reader with an excellent foundation for global and nonlinear algebra.

Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time).