Differential calculus and equations

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

Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology.

With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientifi

This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas.

This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain.

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance.

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations.

This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems.

Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors.

Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198].

This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.

With the collapse of Demographic Transition Theory, new theories of population must not just be explanations, but should be falsifiable theories which can compute the number of occurrences of marriages and births.

This is a collection of lectures by leading research mathematicians on the very latest work on qualitative theory of solutions of dynamical systems, ordinary differential equations, delay-differential equations, Volterra integrodifferential equations and partial differential equations.

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions.

This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems.

This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations.

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role.

Epitaxy is a very active area of theoretical research since several years.

This self-contained book addresses the three most popular computational methods in CAE (finite elements, boundary elements, collocation methods) in a unified way, bridging the gap between CAD and CAE.

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order.

The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations.

Straightforward introduction for non-specialists and experts alike.

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations.

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

Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few.

Classification and Examples of Differential Equations and their Applications is the sixth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set.

This text was the first book on the Lévy Laplacian that generalized classical work and could be widely applied.

Andreas Potschka discusses a direct multiple shooting method for dynamic optimization problems constrained by nonlinear, possibly time-periodic, parabolic partial differential equations.

First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world.

This book provides a systematic survey of classical and recent results on hyperbolic cross approximation.

This book contains articles presented at the 9th Workshop on Differential-Algebraic Equations held in Paderborn, Germany, from 17-20 March 2019.

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences.

Leonardo wrote, "e;Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics"e;; replace "e;Mechanics"e; by "e;Fluid mechanics"e; and here we are.

The ADI Model Problem presents the theoretical foundations of Alternating Direction Implicit (ADI) iteration for systems with both real and complex spectra and extends early work for real spectra into the complex plane with methods for computing optimum iteration parameters for both one and two variable problems.

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.

Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations.

This study guide is designed for students taking courses in calculus.

Semigroup Theory uses abstract methods of Operator Theory to treat initial bou- ary value problems for linear and nonlinear equations that describe the evolution of a system.

This textbook offers an extensive list of completely solved problems in mathematical analysis.

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

I am sure that something must be found.

This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE).

The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines.

Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.