Differential calculus and equations

This series aims at reporting new developments of a high mathematical standard and of current interest.

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.

Volumes 1A and 1B.

Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes.

This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations.

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.

**2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner**Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies.

A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.

This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics.

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems.

This updated, second edition provides readers with an expanded treatment of the FEM as well as new information on recent trends in rapid prototyping technology.

The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.

The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws.

This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003-2007) "e;Development of Dynamical Mathematics with High Fu- tionality"e; (Program Leader: prof.

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These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff.

This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics.

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial di?

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions.

The general topic of this book is the ergodic behavior of Markov processes.

This text is intended for an honors calculus course or for an introduction to analysis.

This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities.

Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems.

This book collects contributions presented at the INdAM Workshop "e;Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage-MACH2021"e;, held in Rome, Italy in September 2021.

This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics.

This monograph presents a systematic analysis of bubble system mathematics, using the mechanics of two-phase systems in non-equilibrium as the scope of analysis.

Metasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem.

Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations.

This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics.

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.

This volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on continuum mechanics.

This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's problem on existence of a solution to the boundary value problem for the stationary Navier-Stokes system in bounded domains under sole condition of zero total flux.

The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or "e;Gedanken Experiments"e;.

Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors' work on structurally stable planar quadratic polynomial differential systems.

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics.

The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book.

Of considerable importance to numerical analysts, this text contains the proceedings of the 18th Dundee Biennial Conference on Numerical Analysis, featuring eminent analysts and current topics.

This book collects papers mainly presented at the "e;International Conference on Partial Differential Equations: Theory, Control and Approximation"e; (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions.

The goal of this third edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering is the same as previous editions: to provide a good foundation - and a joyful experience - for anyone who'd like to learn about nonlinear dynamics and chaos from an applied perspective.

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

Partial Differential Equations for Mathematical Physicists is intended for graduate students, researchers of theoretical physics and applied mathematics, and professionals who want to take a course in partial differential equations.

Einstein proved that the mean square displacement of Brownian motion is proportional to time.

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty.

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