Differential calculus and equations

The goal of this work is to present the principles of functional analysis in a clear and concise way.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics.

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods.

The implicit function theorem is part of the bedrock of mathematical analysis and geometry.

The objective of this self-contained book is two-fold.

This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation.

?

This book offers a brief, practically complete, and relatively simple introduction to functional analysis.

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics.

This book covers the method of metric distances and its application in probability theory and other fields.

This book offers an ideal graduate-level introduction to the theory of partial differential equations.

The book treats the theory of attractors for non-autonomous dynamical systems.

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday.

?

Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics.

The ADI Model Problem presents the theoretical foundations of Alternating Direction Implicit (ADI) iteration for systems with both real and complex spectra and extends early work for real spectra into the complex plane with methods for computing optimum iteration parameters for both one and two variable problems.

?

The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing.

This book collects some recent developments in stochastic control theory with applications to financial mathematics.

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics.

Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited.

The author's approach is one of continuum models of the aerodynamic flow interacting with a flexible structure whose behavior is governed by partial differential equations.

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems.

This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations.

?

?

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics.

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics.

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions.

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics.

Abstract models for many problems in science and engineering take the form of an operator equation.

Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces.

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years.

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator.

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics.

This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory.

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives.

These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas.

The main aim of this book is to present recent results concerning inequalities of the Jensen, Cebysev and Gruss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S.

This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES.

This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par- tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech- nical Research Council of Turkey and the Middle East Technical University.

This volume of the Proceedings of the congress ISAAC '97 collects the con- tributions of the four sections 1.

There was a time, not long ago, when the only treatment options considered to be worthwhile for patients requiring psychiatric care were the 50-minute hour on the one hand, or full-time hospitalization on the other.

Many problems arising in the physical sciences, engineering, biology and ap- plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces.

This volume consists of papers presented in the special sessions on "e;Complex and Numerical Analysis"e;, "e;Value Distribution Theory and Complex Domains"e;, and "e;Use of Symbolic Computation in Mathematics Education"e; of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997.

There is almost no field in Mathematics which does not use Mathe- matical Analysis.