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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

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The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Differential equations --- Mathematics. --- Math --- Science --- 517.91 Differential equations

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This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience.These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for research, learning and teaching. This volumes consists of seven chapters covering a variet

Differential equations --- Mathematics. --- Math --- Science --- 517.91 Differential equations

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Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

Differential equations. --- 517.91 Differential equations --- Differential equations

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The textbook presents a rather unique combination of topics in ODEs, examples and presentation style. The primary intended audience is undergraduate (2nd, 3rd, or 4th year) students in engineering and science (physics, biology, economics). The needed pre-requisite is a mastery of single-variable calculus. A wealth of included topics allows using the textbook in up to three sequential, one-semester ODE courses. Presentation emphasizes the development of practical solution skills by including a very large number of in-text examples and end-of-section exercises. All in-text examples, be they of a mathematical nature or a real-world examples, are fully solved, and the solution logic and flow are explained. Even advanced topics are presented in the same undergraduate-friendly style as the rest of the textbook. Completely optional interactive laboratory-type software is included with the textbook.

Differential equations. --- Differential Equations. --- 517.91 Differential equations --- Differential equations