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The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and als

Differential equations --- 517.91 Differential equations

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The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discussesthe most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calc

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

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Trends in the theory and practice of non-linear analysis

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

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This book gives students the big picture of calculus. It should be read by prospective and current calculus students and by their teachers. Even someone who has completely mastered the technical side of the subject can benefit from being reminded of the essentially simple ideas and the calculational needs that led mathematicians to develop the rather complex machinery of calculus. Sawyer deals with it all, from what background a student needs to begin, to the study of speed and acceleration, to graphing (slope and curvature), to areas, volumes, and the integral.

Calculus. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- 517 --- 517 Analysis --- Analysis --- Calculus --- Calcul infinitésimal

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The book contains twenty-two original scientific research articles that address the state-of-the-art in using partial differential equations for image and signal processing. The articles arose from presentations given at the international conference on PDE-Based Image Processing and Related Inverse Problems, held at the Centre of Mathematics for Applications, University of Oslo, Norway, August 8-12, 2005. The purpose of the conference was to bring together international - searchers to present various aspects of new developments in using numerical techniques for partial differential equations to analyse and process digital - ages. Various aspects of new trends and techniques in this field were discussed in the conference, covering the following topics: • Level set methods and applications • Total variation regularization and other nonlinear filters • Noise analysis and removal • Image in painting • Image dejittering • Optical flow estimation • Image segmentation • Image registration • Analysis and processing of MR images and brain mapping • Image construction techniques • Level set methods for inverse problems Inverse problems for partial differential equations have large areas of app- cations. Although image analysis and PDE inverse problems seem to be - related at a first glance, there are many techniques used in one of these two areas that are useful for the other. One goal of the conference was to highlight some of the recent efforts in merging some of the techniques for these two research areas.

Image processing --- Differential equations --- Digital techniques --- 517.91 Differential equations