Calculus and mathematical analysis

The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis.

Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory.

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems.

Geometric measure theory has roots going back to ancient Greek mathematics, for considerations of the isoperimetric problem (to ?

Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc.

make it look much more logical, but actually it happens quite differently.

Since the ?

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.

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers.

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.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, algorithms and sequence design.

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 is both a text and a paean to twentieth-century real variables, measure theory, and integration theory.

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?

Enrique Castillo is a leading figure in several mathematical and engineering fields, having contributed seminal work in such areas as statistical modeling, extreme value analysis, multivariate distribution theory, Bayesian networks, neural networks, functional equations, artificial intelligence, linear algebra, optimization methods, numerical methods, reliability engineering, as well as sensitivity analysis and its applications.

This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space.

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

Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject.

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.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

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 volume contains the first two out of four chapters which are intended to survey a large part of the theory of theta functions.

This book contains 104 of the best problems used in the training and testing of the U.

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

This book evolved from a one-year sequence of courses offered by the authors at Iowa State University.

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).

This monograph, derived from an advanced computer science course at Stanford University, builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions.

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?

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