How is f(x, y) read

what does it mean?

what should i look up to find out more

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- Jan 24th 2010, 10:58 AM #1

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- Jan 24th 2010, 11:02 AM #2
it is read (spoken): "f of x y" or "f of x and y" in my experience. it means f is a function of x and y. that is, a function with two independent variables. look up multivariable functions. functions of this type, particularly "f(x,y)" first become common in a calculus 3 course.

- Jan 25th 2010, 06:42 AM #3

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For example, f(x,y)= 3x+ 2y and $\displaystyle g(x,y)= x^2+ y^2$ are functions of two variables. f(1, 2)= 3(1)+ 2(2)= 3+ 4= 7 and $\displaystyle g(2, 3)= 2^2+ 3^2= 4+ 9= 9$. Quite often you can think of z= f(x,y) as defining a surface. At each value of x and y, z is the height of the surface above (or below is f(x,y) is negative) the xy-plane.

For these examples, f(x,y)= 3x+ 2y is the equation of a plane and $\displaystyle g(x,y)= x^2+ y^2$ is a "paraboloid".

(f(x,y), in general, doesn't have anything to do with Number Theory.)

- Jan 25th 2010, 09:08 AM #4

- Jan 25th 2010, 04:41 PM #5

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Thanks, I thought it had something to do with binary relations.

I've also noticed that graphing such functions is quite difficult. I saw that you said that " is a "paraboloid"." Can I guess the shape of a function by looking at the degree of the variables of the function i.e. would g(x, y) = x^3 + y^3 be some sort of hour-glass shape?

(Some background on these seemingly simple questions: I'm a first year physics student, I walked into the wrong lecture room and was too ashamed to get up in the middle of a class so I stayed and learned something about PDE's. Not much, but something... Partial derivatives actually make a lot of sense in the context of geometry- I would always get really pissed whenever I would encounter a related rates question in highschool calc involving geometry where a height variable would be held constant- now with partial differentiation I don't have to answer one part of the question... anyway, thanks)

- Jan 25th 2010, 11:36 PM #6

- Jan 26th 2010, 11:52 AM #7

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- Jan 26th 2010, 11:47 PM #8

- Jan 26th 2010, 11:56 PM #9

- Jan 27th 2010, 04:11 AM #10

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Well, yes, binary relations are relations on two variables, not necessarily functions. But functions and relations of two variables includes far more than binary relations, just as partial derivatives are used in far more than partial differential equations.

When I was in graduate school, this really, really, young guy came into the class room. I guessed he was an undergraduate, probably a freshman, who had come into the wrong room and wondered if he would have the courage to leave when he discovered his error. It turned out he was the**professor**!

- Jan 27th 2010, 04:43 AM #11
As he's a physics student, he'll probably learn Maxwell's equations soon (second year of an undergrad degree), which are PDE. The same apply for the "Heat equation".

I remember I was having a calculus 3 course along with a physics course involving the heat equation... I'm almost sure it's common.