Symbolic mathematics

Journal of Chemical Education Symbolic Mathematics in Chemistry http //jchemed.chem.wisc.edu/JCEDLib/SymMath/index.html... 

A survey of computer use in university courses has been carried out by Miles and Francis 149). Due to poor response rate of a Web-based questionnaire, the findings were skewed toward those faculty members who were using computers in their course. The most widely used application among the respondents was the spreadsheet, while the use of molecular modeling, and symbolic mathematics software lagged behind. The authors recommended that teachers should develop more computer-based activities, exploit fully the Web resources, and transfer effectively technical skills. They also provided a list of relevant Web sites, but in the time elapsed since that publication, the currently available Web material must be greatly enhanced, both in terms of number of materials available and in terms of quality of content. 

In this project students review the Chapman cycle mechanism in detail and some photochemistry concepts including the photostationary state. A key element of this project is its focus on an important chemical mechanism and the use of exploratory options for predicting ozone concentrations as a function of time while reviewing other fundamental chemical kinetics concepts. Mathcad is used as the symbolic mathematics engine for solving the requisite differential equations and ample instruction is provided to students to guide them on the use of the software in this project. 

Working this problem is greatly facilitated by symbolic mathematical software.)... 

Note The tedium of completing such exercises, as well as following many derivations in this book, is reduced by the use of symbolic mathematical software. We recommend that students gain a working familiarity with at least one package such as Mathematica , MATLAB , Mathcad , or the public-domain package MAXIMA. 

To obtain a complete drug concentration profile, both the input and disposition kinetics must be known or assumed. If the input is an intravenous bolus, zero or first order, and disposition is first order, then the input and disposition can be combined mathematically through the convolution operation, represented by the symbol. Mathematically, this is represented as... 

More complex enzymatic reactions usually display Michaelis-Menten kinetics and can be described by Eq. (2). However, the forms of constants Km and Vm can be very complicated, consisting of many individual rate constants. King and Altman (7) have provided a method to readily derive the steady-state equations for enzymatic reactions, including the forms that describe Km and Vm. The advent of symbolic mathematics programs makes the implementation of these methods routine, even for very complex reaction schemes. The P450 catalytic cycle (Fig. 2) is an example of a very complicated reaction scheme. However, most P450-mediated reactions display standard hyperbolic saturation kinetics. Therefore, although the rate constants that determine Km and Vm are... 

As one other example illustrating the power of symbolic mathematics programs. Fig. 6 shows a Mathematica calculation of Franck-Condon factors for the I2 B<— X electronic absorption spectrum studied in Exp. 39. These factors are the squares of the overlap integrals of the vibrational wavefunctions for the lower (v") and upper (v ) vibrational levels involved in a transition ... 

Descriptions of symbolic mathematics programs and some of their applications can be found, for example, in W. H. Cropper, Mathematica Computer Programs for Physical Chemistry, Springer-Verlag, New York (1998) and in J. F. Ogilvie, Mathematics for Chemistry with Symbolic Computation, an electronic text containing Maple worksheets, available at http //www.maplesoft.com. 

Mathematics, in the very broadest sense, is the systematic study of relationships in the physical world and relationships between symbols which need not pertain to the real world. In relation to the world, mathematics is the language of science. It operates within the laws and constraints of science as it examines physical phenomena. Unlike science, however, mathematics has no constraints. So in relation to symbols, mathematics can be considered a pure mental activity which is capable of generating new concepts within the mind unrelated to anything that presently exists. 

Symbolic mathematics, calculus, algebra, differential equations, statistics, geometry, and transforms... 

In this chapter, we discuss symbolic mathematical operations, including algebraic operations on real scalar variables, algebraic operations on real vector variables, and algebraic operations on complex scalar variables. We introduce the concept of a mathematical function and discuss trigonometric functions, logarithms and the exponential function. 

Algebra is a branch of mathematics that was invented by Greek mathematicians and developed by Hindu, Arab, and European mathematicians. It was apparently the first branch of symbolic mathematics. Its great utility comes from the fact that letters are used to represent constants and variables and that operations are indicated by symbols such as x, /, and so on. Operations can be car-... 

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