Methods of Nonlinear Analysis

This graduate textbook derives the theory of convex sets and functions, convex programming, nonlinear convex duality, and generalized convexity, then introduces numerical solution techniques for nonli

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Profes

This proceeding book of Nostradamus conference (http://nostradamus-conference.org) contains accepted papers presented at this event in 2012. Nostradamus conference was held in the one of the biggest a

Hailed as "eminently suitable as a text for a graduate course" by the Bulletin of the American Mathematical Society, this volume offers a survey of the main ideas, concepts, and methods that constitut

This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Its full treatment ranges from smooth to nonsmooth functions, f

This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems arising from such areas as mechanics and fluid dynamics. The book is intended to accompany upper division courses for students of pure and applied mathematics and physics; exercises are consequently included.

This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differentia

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

This is a paperbound edition of a 2000 book about which Book News wrote: Usable for self-study, but primarily intended as a text for one of several undergraduate or graduate control courses that begin