Differential calculus and equations

This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research.

This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter.

This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden.

This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden.

The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form.

The book is the first systematical treatment of the theory of finite elements in Archimedean vector lattices and contains the results known on this topic up to the year 2013.

This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps.

There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic.

This textbook is an elementary introduction to the basic principles of partial differential equations.

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hormander function spaces.

This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems.

The book is the first systematical treatment of the theory of finite elements in Archimedean vector lattices and contains the results known on this topic up to the year 2013.

"e;Higher mathematics"e; once pointed towards the involvement of infinity.

There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic.

This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter.

This textbook is an elementary introduction to the basic principles of partial differential equations.

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid.

Elliptic partial differential equations is one of the main and most active areas in mathematics.

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators.

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hormander function spaces.

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters.

In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations.

The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation.

This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters.

This book deals with analytic treatments of Markov processes.

This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG).

This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years.

This book deals with the general topic "e;Numerical solution of partial differential equations (PDEs)"e; with a focus on adaptivity of discretizations in space and time.

This book is the third volume of three volume series recording the "e;Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"e; taking place in Linz, Austria, October 3-7, 2011.

In recent years, technological progress created a great need for complex mathematical models.

This monograph is a valuable contribution to the highly topical and extremly productive field of regularisation methods for inverse and ill-posed problems.

This is a proceedings of the international conference "e;Painleve Equations and Related Topics"e; which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.

The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs.

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state.

This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich.

Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics.

This is the first part of the second revised and extended edition of the well established book "e;Function Spaces"e; by Alois Kufner, Oldrich John, and Svatopluk Fucik.

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations.

This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces.

The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations.

Green's functions represent one of the classical and widely used issues in the area of differential equations.

The theory of ill-posed problems originated in an unusual way.

The present collection is the very first contribution of this type in the field of sparse recovery.

This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses).