Differential calculus and equations

The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions.

These proceedings are based on the international conference Approximation Theory XVI held on May 19-22, 2019 in Nashville, Tennessee.

This is the second edition of an influential monograph on logarithmic potentials with external fields, incorporating some of the numerous advancements made since the initial publication.

The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense.

This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994.

The parabolic partial differential equations model one of the most important processes in the real-world: diffusion.

A complete introduction to partial differential equations, this is a textbook aimed at students of mathematics, physics and engineering.

Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer.

A selection of surveys and original research papers in mathematical fluid mechanics arising from a 2010 workshop held in Warwick.

Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments.

The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc.

This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method.

This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012.

Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE).

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.

This volume presents a timely overview of control theory and related topics, such as the reconstruction problem, the stability of PDEs, and the Calderon problem.

The concept of higher order derivatives is useful in many branches of mathematics and its applications.

A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm.

Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions.

The Second Edition of Ordinary Differential Equations: An Introduction to the Fundamentals builds on the successful First Edition.

This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research.

Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type.

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations.

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday.

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences.

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations.

Advanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics.

This Brief reports on heat transfer from a solid boundary in a saturated porous medium.

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade.

Dynamical Systems for Biological Modeling: An Introduction prepares both biology and mathematics students with the understanding and techniques necessary to undertake basic modeling of biological systems.

Singular Differential Equations and Special Functions is the fifth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set.

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems.

This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums.

This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies.

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic.

This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes).

Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr.

For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators.

An enormous array of problems encountered by scientists and engineers are based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations.

Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum.

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators.

This volume contains lectures and invited papers from the Focus Program on "e;Nonlinear Dispersive Partial Differential Equations and Inverse Scattering"e; held at the Fields Institute from July 31-August 18, 2017.

Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology.

This volume is devoted to the study of the Navier-Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling.