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Engineering Calculus Notes 425

Engineering Calculus Notes 425 - 2.2 to indicate the...

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4 Mappings and Transformations: Vector-Valued Functions of Several Variables In this chapter we extend differential calculus to vector-valued functions of a vector variable. We shall refer to a rule (call it F ) which assigns to every vector (or point) −→ x in its domain an unambiguous vector (or point) −→ y = F ( −→ x ) as a mapping from the domain to the target (the plane or space). This is of course a restatement of the definition of a function, except that the input and output are both vectors instead of real numbers. 1 We shall use the arrow notation first adopted in
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Unformatted text preview: § 2.2 to indicate the domain and target oF a mapping: using the notation R 2 For the plane and R 3 For space, we will write F : R n → R m to indicate that the mapping F takes inputs From R n ( n ≤ 3) and yields values in in R m ( m ≤ 3). IF we want to speciFy the domain D ⊂ R n , we write F : D → R m . 1 More generally, the notion of a mapping from any set of objects to any (other) set is deFned analogously, but this will not concern us. 413...
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