With the overwhelming use of computers in engineering, science and physics, the approximate solution of complex mathematical systems of equations is almost commonplace. The Best Approximation Method unifies many of the numerical methods used in computational mechanics. Nevertheless, despite the vast quantities of synthetic data there is still some doubt concerning the validity and accuracy of these approximations. This publication assists the computer modeller in his search for the best approximation by presenting functional analysis concepts. Computer programs are provided which can be used by readers with FORTRAN capability. The classes of problems examined include engineering applications, applied mathematics, numerical analysis and computational mechanics. The Best Approximation Method in Computational Mechanics serves as an introduction to functional analysis and mathematical analysis of computer modelling algorithms. It makes computer modellers aware of already established principles and results assembled in functional analysis.

The most commonly used numerical techniques in solving engineering and mathematical models are the Finite Element, Finite Difference, and Boundary Element Methods. As computer capabilities continue to impro' e in speed, memory size and access speed, and lower costs, the use of more accurate but computationally expensive numerical techniques will become attractive to the practicing engineer. This book presents an introduction to a new approximation method based on a generalized Fourier series expansion of a linear operator equation. Because many engineering problems such as the multi dimensional Laplace and Poisson equations, the diffusion equation, and many integral equations are linear operator equations, this new approximation technique will be of interest to practicing engineers. Because a generalized Fourier series is used to develop the approxi mator, a "best approximation" is achieved in the "least-squares" sense; hence the name, the Best Approximation Method. This book guides the reader through several mathematics topics which are pertinent to the development of the theory employed by the Best Approximation Method. Working spaces such as metric spaces and Banach spaces are explained in readable terms. Integration theory in the Lebesque sense is covered carefully. Because the generalized Fourier series utilizes Lebesque integration concepts, the integra tion theory is covered through the topic of converging sequences of functions with respect to measure, in the mean (Lp), almost uniformly IV and almost everywhere. Generalized Fourier theory and linear operator theory are treated in Chapters 3 and 4."

Fashionably late, Tommy v2 and Zor bring you our first book What is the measure of success? How do you achieve it? Having your grubby little talons on this book is a hell of a start, that's for sure. With our extensive life experience (plus learning from someone else's mistakes, of course) and absurd insight into the obvious, we will take you on a rollercoaster ride to self-improvement and enlightenment, all without waiting in line with teenagers that keep calling each other 'trans-bro-mers' or something equally fantastic. We cut through the crap and deliver the straight goods right into your eager brain. We will teach you our proprietary formula that can be applied to all facets of life to help each and every one of you succeed with the least amount of effort required. This isn't self-help, this is us helping you

The 5:2 Fast is rapidly growing in popularity for its ability to promote weight loss without feeling deprived. The basic principle is very simple: eat normally for five days a week and restrict calories for two non-consecutive days. That's it. The trick is to eat healthy on non-fast days and cut calories to 500 for women and 600 for men during fast days. Easy enough right? The main problem people run into is how to maximize their calorie allowance on fast days. It's easy to blow a 500-calorie budget by eating half a cup of cashews, leaving you hungry for the rest of the day, not to mention the low nutritional value of eating a single type of food for an entire day. We came up with the perfect solution: a collection of 30 nutrient-dense recipes that are help you make the most of your fast day calorie allowance. This cookbook contains 30 all-natural low-calorie recipes.