Calculus and mathematical analysis

These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems.

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA.

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent.

The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions.

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampere and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view.

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere.

The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes.

This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory.

This volume aims to disseminate a number of new ideas that have emerged in the last few years in the field of numerical simulation, all bearing the common denominator of the "e;multiscale"e; or "e;multilevel"e; paradigm.

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V.

In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.

At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.

This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation.

Spectral theory of bounded linear operators teams up with von Neumann's theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators.

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011.

This book presents the foundations of the inverse scattering method and its applications to the theory of solitons in such a form as we understand it in Leningrad.

Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve.

This book combines two mathematical branches: dynamical systems and radialbasisfunctions.

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems.

This book presents topics of science and engineering which occur in nature or are part of daily life.

This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems.

Special functions and orthogonal polynomials in particular have been around for centuries.

This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field.

These notes deal with deformation theory of complex analytic singularities and related objects.

The proceedings of the Israeli GAFA seminar on Geometric Aspect of Functional Analysis during the years 2001-2002 follow the long tradition of the previous volumes.

Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets).

Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications.

Preface to the First Edition This textbook is an introduction to Scienti?

This volume introduces some basic theories on computational neuroscience.

The author develops a deformation theory for degenerations of complex curves; specifically, he treats deformations which induce splittings of the singular fiber of a degeneration.

Many of problems of the natural sciences lead to nonlinear partial differential equations.

Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices.

This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups.

This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy.

Hofstadter's Law: It always takes longer than you think it will take, even if you take into account Hofstadter's Law.

No book is born in a vacuum.

This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics.

In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction - for an audience knowing basic functional analysis and measure theory but not necessarily probability theory - to analysis in a separable Hilbert space of infinite dimension.

Applied Mathematics: Body&Soul is a mathematics education reform p- gram including a series of books, together with associated educational ma- rial and open source software freely available from the project web page at www.

The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis.

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids.

In the last few years there has been a growing interest in the development of numerical techniques appropriate for the approximation of differential model problems presenting multiscale solutions.

This book summarizes and highlights progress in our understanding of Dy- namical Systems during six years of the German Priority Research Program "e;Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems"e; .

High-Performance Computers (HPC) have initiated a revolutionary develop- ment in research and technology since many complex and challenging prob- lems in this area can only be solved by HPC and a network in modeling, algo- rithms and software.