Algebra, scientific

This appendix introduces two mathematics topics important for chemistry students scientific ebra and electronic calculator mathematics. The scientific algebra section (Sec. A.l) presents the relationships between scientific algebra and ordinary algebra. The two topics are much more similar than different however, since you already know ordinary algebra, the differences are emphasized here. The calculator math sectitm (Sec. A.2) discusses points with which students most often have trouble. This section is not intended to replac the instruction booklet that comes with a calculator, but to emphasize the points in that booklet that are moslj important to science students. 

For more practice with the concepts in this appendix, you might recalculate the answers t() some of the examples the text. 

We then isolate the variable by multiplication or division. In this case, we divide by 5  

If values are given for some variables, for example, for the equation 

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Perhaps the biggest difference between ordinary algebra and scientific algebra is that scientific measurements (and most other measurements) are always expressed with units. Like variables, units have standard symbols. The units are part of the measurements and can often help determine what operation to perform. 

Scientific algebra is very similar to ordinary algebra, except that letters are used that suggest the variables they represent. For example, d is used for density and m is used for mass. We can solve equations for cf or m in just the way we can for x or y. 

Petzold, L. R. A Description of DASSL A Differential-Algebraic System Solver, Sandia National Laboratory Report SAND82-8637 also in Stepleman, R. S. et al., eds. IMACS Trans, on Scientific Computing, vol. 1, pp. 65-68. 

The purpose of this Chapter is not to present an exhaustive theory of linear algebra that would take more than a volume by itself to be presented adequately. It is rather to introduce some fundamental aspects of vectors, matrices and orthogonal functions together with the most common difficulties that the reader most probably has encountered in scientific readings, and to provide some simple definitions and examples with geochemical connotations. Many excellent textbooks exist which can complement this introductory chapter, in particular that of Strang (1976). 

Bohm, A., Ne eman, Y., and Barut, A. O. (1988), Dynamical Groups and Spectrum Generating Algebras, World Scientific, Singapore. 

Pavelle, R. Rothstein, K. Fitch, J.P. Computer Algebra. Scientific American 1981, 245. 

Pelzold, L. R., Differential/algebraic equations are not ODEs, SIAM Journal on Scientific and Statistical Computing, No. 3, pp. 367-385 (1982). 

Lazman M., and Yablonsky G. Computer algebra in chemical kinetics Theory and application. Computer algebra in Scientific computing. Proceedings of CASC 2004, Muenchen, 313-324 (2004). 

Supported by the Netherlands Organisation for Scientific Research (N.W.O.),in the project Arithmetic Algebraic Geometry... 

M. Lesser, The Analysis of Complex Nonlinear Mechanical Systems. A Computer Algebra Approach, World Scientif Publishing Co. (1995), ISBN 981-02-2209-2. 

Chemistry and physics are both very logical sciences, but both depend on math to translate concepts into application. Unfortunately, many students who struggle in these disciplines have more trouble with the mathematics than with the scientific concepts. Therefore, let us begin our exploration of chemistry and physics with a review of some basic math skills and concepts that you will use throughout this course. While this chapter reviews basic math skills, it cannot replace a basic understanding of college-level algebra. 

This chapter will review the fundamental mathematical concepts (algebra and trigonometry) needed for a quantitative understanding of college-level chemistry and physics. Virtually all of this material is covered in high-school mathematics classes, but often the connection to real scientific applications is not obvious in those classes. In contrast, the examples used here will frequently involve chemical and physical concepts that will be covered in detail in later chapters or in the later parts of a standard freshman chemistry book. Here they will be treated as math problems later you will see the underlying chemistry. 

In this unit you will find explanations, examples, and practice dealing with the calculations encountered in the chemistry discussed in this book. The types of calculations included here involve conversion factors, metric use, algebraic manipulations, scientific notation, and significant figures. This unit can be used by itself or be incorporated for assistance with individual units. Unless otherwise noted, all answers are rounded to the hundredth place. The calculator used here is a Casio FX-260. Any calculator that has a log (logarithm) key and an exp (exponent) key is sufficient for these chemical calculations. 

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