Free E-Books: Mathematics

Mathematics and CAD: Numerical Methods for CAD by Yvon Gardan

This book introduces mathematical bases in a general way, so as to allow the reader to understand the basic tools. Based on the-work of leading French researchers, it gives a clear outline of the mathematical concepts employed in setting up a CAD system that uses interactive graphic techniques.
It deals thoroughly with basic graphics, two- and three-dimensional operations, as well as considering mathematical modeling in relation to geometric modeling. It also examines curves and surfaces, numerical methods of solving equations and finite element modeling, one of the many CAD design tools available today. Contents: Part 1: Basic Problems Using Graphics. Part 2: Curves and Surfaces. Part 3: Numerical Methods for Solving Equation Systems. Part 4: The Finite Element Model. Yvon Gardan, who is Professor of Computer Science at the University of Metz, is a wellknown authority on interactive graphic techniques, and is the author of Interactive Graphics in CAD. He is also director of the CADCAM Association of France (MICADO).

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Boundary Stabilization of Thin Plates (Studies in Applied and Numerical Mathematics)

Boundary Stabilization of Thin Plates provides a comprehensive and unified treatment of asymptotic stability of a thin plate when appropriate stabilizing feedback mechanisms acting through forces and moments are introduced along a part of the edge of the plate.

In particular, primary emphasis is placed on the derivation of explicit estimates of the asymptotic decay rate of the energy of the plate that are uniform with respect to the initial energy of the plate, that is, on uniform stabilization results.
The method that is systematically employed throughout this book is the use of multipliers as the basis for the derivation of a priori asymptotic estimates on plate energy. It is only in recent years that the power of the multiplier method in the context of boundary stabilization of hyperbolic partial differential equations came to be realized. One of the more surprising applications of the method appears in Chapter 5, where it is used to derive asymptotic decay rates for the energy of the nonlinear von Karman plate, even though the technique is ostensibly a linear one.

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