This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: • Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. • Presents a range of workout examples for better comprehension of spaces and operators. • Algorithms are presented to facilitate computer programming. • Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.

Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.

This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.

Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.

Examines concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies them.

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.