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Wallace_Calculus1

# Wallace_Calculus1 - Math A.1 Physical Properties from a...

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Math R.Wallace, 1/17/03 1 A.1 Physical Properties from a Mathematical Perspective: Single Variable Calculus We may identify two varieties of physical property; those which can be specified by a single number - such as molar mass (i.e. a constant which does not depend on conditions such as temperature, pressure, etc. those which do depend upon conditions and which can be portrayed as a table or graph showing this dependence. In either case all of the numbers involved are real numbers hence physical properties are described by real numbers. In attempting to develop equations which describe our graphs it is often convenient to try to express the variable plotted on the vertical - y axis as some mathematical function of the variable represented on the horizontal - x axis, i.e. we write y f x ´ ( ) In doing so we must always be careful (but often forget) to specify the range of x for which the function might be considered valid. For example, the radius of a circle is, by definition, a positive number; r 0 . So if we are considering a function, say f r r r ( ) = + 1 , there is no point in constructing a graph for r < 0 . This is nonphysical! The next point to note about the graphs we construct is that the “line” drawn through the experimental points is inevitably assumed to be continuous. Thus physical properties exhibit continuous behaviour when subject to small changes in conditions, which, in terms of mathematical language means that physical properties can be represented by continuous functions. A continuous function is one which can be differentiated .

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Wallace_Calculus1 - Math A.1 Physical Properties from a...

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