2224-Sec12_1-HWT

2224-Sec12_1-HWT - Math 2224 Multivariable Calculus Chapter...

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Unformatted text preview: Math 2224 Multivariable Calculus Chapter 12 partial Derivatives Sec. 12.1: Functions of several Variables I. Functions and Variables A. Def n : Suppose D is a set of n-tuples of real numbers (x 1 , x 2 , x 3 ,, x n ). A real-valued function f on D is a rule that assigns a unique (single) real number w=f(x 1 , x 2 , x 3 ,, x n ) to each element in D . The set D is the functions domain. The set of w-values taken on by f is the functions range. The symbol w is the dependent variable of f , and f is said to be a function of the n independent variables x 1 to x n . We also call the x j s the functions input variables and call w the functions output variable. B. One Variable 1. The statement y=f(x) or y is a function of x means y depends on x . 2. x is the independent variable and y is the dependent variable 3. Domain: { x | f(x) is defined} Range: { f(x) | x ! domain} 4. Point: (x,y) C. Two Variables 1. The statement z=f(x,y) or z is a function of x and y means z depends on both x & y....
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This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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2224-Sec12_1-HWT - Math 2224 Multivariable Calculus Chapter...

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