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Wallace_Calculus2

# Wallace_Calculus2 - Math B.1 Physical Properties dependent...

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Math R.Wallace, 1/17/03 16 B.1 Physical Properties dependent upon more than one variable. (This material lies beyond courses such as 13.139, 13.149. We do not need to know very much - just enough to be familiar with the language.) B.1.1 Differential Calculus of Functions of Two Variables. (Reference for the interested student: “ Modern Mathematical Analysis ” by Protter and Morrey, Addison Wesley.) We have previously reviewed the calculus of functions of a single variable, f x ( ) . Circumstances arise in which we are interested in functions of more than one variable. The simplest such case relates to functions of two variables, f x y ( , ) where x and y denote independent variables. As examples we can consider the functions 1. f x y xy ( , ) = 2. f x y x y ( , ) = + 2 3 3. f x y x y xy ( , ) = 2 2 3 One can think of defining two kinds of derivatives of such functions, a derivative with respect to the variable x , and a derivative with respect to the variable y . To show how this can be realized we proceed as follows B.1.1.1 Partial derivatives We shall follow example 3 above. You can try them all.

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Wallace_Calculus2 - Math B.1 Physical Properties dependent...

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