Some Useful Mathematics

Mattis, D. C. The Theory of Magnetism Made Simple An Introduction to Physical Concepts and to Some Useful Mathematical Methods, World Scientific Publishing Company New York, 2006. Lefteri, C. Arad, Metals Materials for Inspirational Design, Rotovision London, 2004. 

This book will acquaint the reader with some of the important tools and strategies now available for investigating chemical processes and systems on personal computers. We present some useful mathematical models, numerical methods for solving them, and statistical methods for testing and discriminating candidate models with experimental data. The software package Athena Visual Studio, obtained from www.AthenaVisual.com, will enable you to do these computations and view the results on your personal computer screen, print them and transmit them. Familiarity with Microsoft Windows (1998 or later) is required, but little knowledge of Fortran, since Athena converts equation statements directly into Fortran code as described in the Athena tutorial on your computer s desktop. 

There is an important mathematical concept called uniform convergence. If a functional series converges in some interval, it is uniformly convergent in that interval if it converges with at least a certain fixed rate of convergence in the entire interval. We do not discuss the details of this concept. If a functional series is uniformly convergent in some interval, it has been shown to have some useful mathematical properties, which we discuss later. 

Thermodynamics is a quantitative subject. It allows us to derive relations between the values of numerous physical quantities. Some physical quantities, such as a mole fraction, are dimensionless the value of one of these quantities is a pure number. Most quantities, however, are not dimensionless and their values must include one or more units. This chapter reviews the SI system of units, which are the preferred units in science applications. The chapter then discusses some useful mathematical manipulations of physical quantities using quantity calculus, and certain general aspects of dimensional analysis. 

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