Differential calculus and equations

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "e;Intensive Research Program on Advances in Nonsmooth Dynamics 2016"e;, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 1st to April 29th, 2016.

This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (Korovkin-Type) Approximation Theory, and Partial Differential Equations.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems.

This book is intended as a self-contained exposition of hyperbolic functional dif- ferential inequalities and their applications.

This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm-Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations).

This monograph presents results of the analytical and numerical modeling of convective heat and mass transfer in different rotating flows caused by (i) system rotation, (ii) swirl flows due to swirl generators, and (iii) surface curvature in turns and bends.

This book is focused on modeling with linear differential equations with constant coefficients.

The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators.

The aim of this book is to explain, analyze and compute the kinds of motions that appear in an extended vicinity of the geometrically defined equilateral points of the Earth-Moon system, as a source of possible nominal orbits for future space missions.

Difference Equations or Discrete Dynamical Systems is a diverse field which impacts almost every branch of pure and applied mathematics.

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago.

This book presents a detailed development of the divergence theorem.

In this book we analyze  relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics.

In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations.

This book contains a comprehensive collection of chapters on recent and original research, along with review articles, on mathematical modeling of dynamical systems described by various types of differential equations.

This book is concerned with the study in two dimensions of stationary solutions of u?

Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science.

A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes.

This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems.

This book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019.

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds.

Extending and generalizing the results of rational equations,Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their p

This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.

This book surveys some topics in the rapidly developing areas of regular and singular boundary value problems.

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "e;Elementary Partial Differential Equations"e; or "e;Boundary Value Problems"e;.

This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e.

A compact treatment that takes the reader from simple examples to current research involving ordinary differential equations.

The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations.

In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition.

The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann-Roch-Grothendieck for proper submersions.

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences.

Based on the Working Conference on Boundary Control and Boundary Variation held in Sophia-Antipolis, France, this work provides important examinations of shape optimization and boundary control of hyperbolic systems, including free boundary problems and stabilization.

The main new feature of the fifth edition is the addition of a new chapter, Chapter 12, on applications to mathematical finance.

No detailed description available for "e;A New Class of Singular Integral Equations and Its Application to Differential Equations with Singular Coefficients"e;.

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This book gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021.

This book describes the basic principles of Clean Numerical Simulation (CNS) proposed by the author in 2009, as well as several of its applications.

This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group.

This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator.

Presents a systematic study of the common zeros of polynomials in several variables which are related to higher dimensional quadrature.

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

This book provides a systemic and self-contained guide to the theoretical description of the fundamental properties of plasmonic waves.

The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018.

This is the first book devoted to the task of computing integrability structures by computer.