Differential calculus and equations

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain.

This book features a selection of articles by Louis Boutet de Monvel and presents his contributions to the theory of partial differential equations and analysis.

In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators.

The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions.

Perturbed functional iterations (PFI) is a large scale nonlinear system solver.

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.

The book collects relevant contributions presented at a conference, organized in honour of Carlo Cercignani, that took place at Politecnico di Milano on May 24-28, 2021.

This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations.

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations.

This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes.

The book aims to provide a comprehensive understanding of the most recent developments in finite volume methods.

Presents concepts of chaotic systems for researchers and graduate students in statistical mechanics and chaos.

This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view.

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science.

The theory and applications of Iteration Methods is a very fast-developing field of numerical analysis and computer methods.

The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation.

A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics.

The book serves as a primary textbook of partial differential equations (PDEs), with due attention to their importance to various physical and engineering phenomena.

Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences.

Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest.

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis.

Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated.

One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system.

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This book provides a systematic and thorough overview of the classical bending members based on the theory for thin beams (shear-rigid) according to Euler-Bernoulli, and the theories for thick beams (shear-flexible) according to Timoshenko and Levinson.

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday.

This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.

In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis.

The heart of the book is the development of a short-time asymptotic expansion for the heat kernel.

Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations.

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).