Differential calculus and equations

This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines.

Dieses Buch befaßt sich mit der mathematischen Analyse von dynamischen Prozes­ sen, deren zeitliche Entwicklung nicht kontinuierlich fließend, sondern in diskreten Zeit­ schritten modelliert wird.

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.

The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results.

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.

Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability.

This monograph presents a synopsis of fluid dynamics based on the personal scientific experience of the author who has contributed immensely to the field.

This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems.

This volume contains the texts of the four series of lectures presented by B.

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises.

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations.

This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author's works and his joint works with his former students.

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 book provides an introduction to the broad topic of the calculus of variations.

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V.

This book provides an introduction to the structure and stability properties of solutions of functional differential equations.

Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations.

This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems.

This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity.

This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others.

These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula.

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

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena.

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.

A first course in ordinary differential equations for mathematicians, scientists and engineers.

Indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial  structure of complicated systems.

This book offers an essential introduction to the mathematical theory of compressible viscous fluids.

This book collects the abstracts of  the mini-courses and lectures given during the Intensive Research Program "e;Spaces of Analytic Functions: Approximation, Interpolation, Sampling"e; which was held at the Centre de Recerca Matematica (Barcelona) in October-December, 2019.

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems.

This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings.

This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs.

This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods.

Advanced Problem Solving Using Maple(TM): Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models.

This textbook is devoted to second order linear partial differential equations.

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

The First Pan-China Conference on Differential Equations was held in Kunming, China in June of 1997.

This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

This book introduces an interesting and alternative way to design absorbing boundary conditions (ABCs) for quantum wave equations, basically the nonlinear Schrodinger equation.

Thismonographisintendedasasimpleintroductiontotheso-calledLULU-theory and the practical use of LULU-smoothers leading up to a full Multiresolution Analysis of any ?

As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998.

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place.

Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics.