Calculus and mathematical analysis

Networked systems are all around us.

This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic.

Since the birth of the Chua circuit in 1983, a considerable number of fruitful, fascinating and relevant research topics have arisen.

This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology.

Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest.

This book (Vista II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions.

Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations.

Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research.

The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions.

This book contains the contributions by the participants in the nine of a series of workshops.

The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals.

In many physical problems several scales are present in space or time, caused by inhomogeneity of the medium or complexity of the mechanical process.

The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces.

In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz' infinitesimal calculus.

This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal.

This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle.

This volume contains a selection of contributions by prominent mathematicians from the many interesting presentations delivered at the Conference of Mathematics and Mathematical Physics that was held in Fez, Morocco duing the period of 28-30 October, 2008.

This book describes the development of a constitutive modeling platform for soil testing, which is one of the key components in geomechanics and geotechnics.

The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs).

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997.

This monograph presents univariate and multivariate classical analyses of advanced inequalities.

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications.

This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations.

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009.

The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago.

Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors.

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date.

In the last forty years, nonlinear analysis has been broadly and rapidly developed.

This proceedings is a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory.

New Edition: Fractional Calculus: An Introduction for Physicists (3rd Edition)Fractional calculus is undergoing rapid and ongoing development.

This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory.

The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan.

This is the only book that deals comprehensively with fixed point theorems throughout mathematics.

The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields.

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering.

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda's 60th birthday.

This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrodinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations.

This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others.

The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications.

The focus of this is on the latest developments related to the analysis of problems in which several scales are presented.

This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set.

In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.

This book provides a broad introduction to the generalized inverses, Moore-Penrose inverses, Drazin inverses and T-S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional.

Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly.

This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions.

This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind.

Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences.

This book is an introductory text on real analysis for undergraduate students.

This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems.

A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.