Engineering Calculus Notes 227

Engineering Calculus Notes 227 - 3 Differential Calculus...

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Unformatted text preview: 3 Differential Calculus for Real-Valued Functions of Several Variables In this chapter and in Chapter 5, we consider functions whose input involves several variables—or equivalently, whose input is a vector—and whose output is a real number. We shall restrict ourselves to functions of two or three variables, where the vector point of view can be interpreted geometrically. A function of two (resp. three) variables can be viewed in two slightly different ways, reflected in two different notations. We can think of the input as three separate variables; often it will be convenient to use subscript notation xi (instead of x, y, z ) for these variables, so we can write f (x, y ) = f (x1 , x2 ) in the case of two variables and f (x, y, z ) = f (x1 , x2 , x3 ) in the case of three variables. → Alternatively, we can think of the input as a single vector − formed from x listing the variables in order: → − = (x, y ) = (x , x ) x 1 215 2 ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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