Calculus and mathematical analysis

This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces.

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications.

The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations.

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Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics.

This work is a concise introduction to spectral theory of Hilbert space operators.

Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means of encoding isotropic phenomena.

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables.

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume.

Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals.

The modern subject of differential forms subsumes classical vector calculus.

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels.

This comprehensive textbook is intended for a two-semester sequence in analysis.

This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity.

The contributions in this volume-dedicated to the work and mathematical interests of Oleg Viro on the occasion of his 60th birthday-are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap among analysis, geometry, and topology.

The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications.

This book comprises five parts.

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others.

Reprinted as it originally appeared in the 1990s, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics.

Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields.

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations.

An enormous array of problems encountered by scientists and engineers are based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations.

This book presents the general theory of categorical closure operators to- gether with a number of examples, mostly drawn from topology and alge- bra, which illustrate the general concepts in several concrete situations.

One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem.

The development of time scales is still in its infancy, yet as inroads are made, interest is gathering steam.

Algebraic, differential, and integral equations are used in the applied sciences, en- gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time.

The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har- monic analysis to basic applications.

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First posed by Hermann Weyl in 1910, the limit-point/limit-circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations.

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};' It is intended to serve as an intro- duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layers developed in (MZl].

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis.

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application.

Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz's proof of the isoperimetric inequality using Fourier series.

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings.

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer- sity of Cambridge.

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences.

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Probably I ought to explain why one more book on numerical methods can be useful.

It is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana- lytic Functions.

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Optimal control of partial differential equations (PDEs) is a well-established discipline in mathematics with many interfaces to science and engineering.

The subject of real analysis dates to the mid-nineteenth century - the days of Riemann and Cauchy and Weierstrass.

Here is a book that will be a joy to the mathematician or graduate student of mathematics or even the well-prepared undergraduate who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis.

This monograph presents extensions of the Moser-Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen-Cahn PDE model of phase transitions.

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems.