Differential calculus and equations

This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering.

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.

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself.

The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics.

A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations.

"e;This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology.

This monograph offers the first systematic account of (metric) regularity theory in variational analysis.

This book discusses the state-of-the-art and open problems in computational finance.

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Grobner bases) and geometry (via quiver theory).

This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs.

This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations.

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.

The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis.

This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems.

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This volume provides a comprehensive review of multiple-scale dynamical systems.

This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations.

This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite.

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019.

Introductory Differential Equations, Fifth Edition provides accessible explanations and new, robust sample problems.

This book is devoted to unstable solutions of stochastic differential equations (SDEs).

This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals.

This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S.

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems.

This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016.

This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier-Stokes equations.

Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs).

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes-parabolic and hyperbolic.

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This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem.

Differential equations play an important role in modelling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons.

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.

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions.

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods.

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales.

Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems.

Boundary Element Method for Plate Analysis offers one of the first systematic and detailed treatments of the application of BEM to plate analysis and design.

Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures.

In the study of Magnetic Positioning Equations, it is possible to calculate and create analytical expressions for the intensity of magnetic fields when the coordinates x, y and z are known; identifying the inverse expressions is more difficult.

Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications.

Optimal control theory has numerous applications in both science and engineering.

This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence.

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.

Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments.

This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences.

This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids.

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation.

Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations.