Differential calculus and equations

Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory.

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type.

Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one.

The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems.

Financial Mathematics is an exciting, emerging field of application.

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data.

Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables.

the solution or its gradient.

Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type.

The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension.

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Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph.

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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 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.

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.

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

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.

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

This volume introduces some basic theories on computational neuroscience.

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

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

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.

Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us.

This text gathers, revises and explains the newly developed Adomian decomposition method along with its modification and some traditional techniques.

This text gathers, revises and explains the newly developed Adomian decomposition method along with its modification and some traditional techniques.

For over fifty years, Boundary Value Problems and Partial Differential Equations, Seventh Edition has provided advanced students an accessible and practical introduction to deriving, solving, and interpreting explicit solutions involving partial differential equations with boundary and initial conditions.

The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance.

An introduction to the basic theory of stochastic calculus and its applications.

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time.

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations.

Mehr als 700 typische Klausur- und Übungsaufgaben zur Höheren Mathematik für Ingenieure, Natur- und Wirtschaftswissenschaftler mit detaillierten Lösungen ermöglichen eine optimale Vorbereitung auf Prüfungen und erleichtern die Bearbeitung von Übungsblättern.

This book discusses the fundamentals of the numerics of parabolic partial differential equations posed on network structures interpreted as metric spaces.

This book discusses the fundamentals of the numerics of parabolic partial differential equations posed on network structures interpreted as metric spaces.

This book contains chapters of the proceedings presented at the UiTM International Conference of Mathematical Sciences 2024 (UICMS 2024), organized by Universiti Teknologi MARA (UiTM), Shah Alam, Selangor, Malaysia, from October 12–13, 2024.

This proceedings volume convenes works within the field of fractional calculus and its applications, presented at the International Conference on Fractional Differentiation and its Applications (ICFCA), held in Sousse, Tunisia, from December 26th to 30th, 2024.