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Many Variables

In the function z = f(x,y) there are two independent variables, x and y and one dependent variable z. In practice, though, we can have functions of as many variables as we like. For example, the temperature outside depends not only on location (latitude and longitude) but also on time of day. Your grade in class is a function of your homework, quiz, test, and final exam scores. Functions can be as simple or as complicated as necessary. However, representing functions of more than two variables graphically or as a numerical table requires a bit more work. Try to figure out a good way to represent the function w = f(x,y,z) as a numerical table. You'll find that you need several different tables to completely capture the function. Algebraic functions do not suffer this particular drawback, although they tend to be much more abstract.



Vector Calculus
1/7/1998