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This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields s

Mathematical analysis --- Differential equations --- 517.91 Differential equations --- 517.1 Mathematical analysis

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Provides useful tools in Lie group analysis to solve nonlinear partial differential equations. This work presents many of the important issues in nonlinear wave dynamics and nonlinear fluid mechanics. It also discusses fundamental problems and theories in classic and quantum dynamical systems.

Mathematical analysis --- Nonlinear theories --- 517.1 Mathematical analysis

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This work focuses on equations with partial derivatives and the regularity of the solutions of their resolutions.

Differential equations. --- Functional differential equations. --- Differential equations, Functional --- Differential equations --- Functional equations --- 517.91 Differential equations

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Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.

Functional analysis --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Analyse fonctionnelle --- Global analysis (Mathematics). --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis

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This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.

Mathematics. --- Mathematics, general. --- Functions of real variables. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Real variables --- Functions of complex variables --- Math --- Science