Abstract
This chapter presents the application of variables and functions in physical chemistry. The ensemble of rational and irrational numbers is called “real numbers.” The sum, difference, and product of two real numbers are real. The division of two real numbers is defined in all cases except in the division by zero. The chapter examines the independent variable and the dependent variable by the way measurements are made and, mathematically, on the presentation of the experimental data. The properties and classification of functions are described in the chapter. Functions are classified as either algebraic or transcendental. Algebraic functions are rational integral functions or polynomials, rational fractions or quotients of polynomials, and irrational functions. Some of the simplest functions in the last category are those formed from rational functions by the extraction of roots. The more elementary transcendental functions are exponentials, logarithms, trigonometric, and inverse trigonometric functions. Examples of these functions are discussed in the chapter. Another family of functions discussed is the hyperbolic functions, which can also be derived from the exponential. They are analogous to the circular functions. The various relations among the hyperbolic functions can be derived for the circular functions.
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