Differential calculus and equations

In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity.

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

Harmonic analysis is a venerable part of modern mathematics.

I am sure that something must be found.

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade.

The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games.

The purpose of the book is to summarize Lyapunov design techniques for nonlinear systems and to raise important issues concerning large-signal robustness and performance.

This book introduces geometric spectral theory in the context of Riemann surfaces.

The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear partial di?

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.

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.

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.

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 ?