# Thread: What does this mean: f(x, y)

1. ## What does this mean: f(x, y)

what does it mean?
what should i look up to find out more

2. Originally Posted by Noxide
what does it mean?
what should i look up to find out more
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.

3. For example, f(x,y)= 3x+ 2y and $g(x,y)= x^2+ y^2$ are functions of two variables. f(1, 2)= 3(1)+ 2(2)= 3+ 4= 7 and $g(2, 3)= 2^2+ 3^2= 4+ 9= 9$. 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 $g(x,y)= x^2+ y^2$ is a "paraboloid".

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

4. Originally Posted by HallsofIvy
(f(x,y), in general, doesn't have anything to do with Number Theory.)
I didn't even notice that. Hehe, moved

5. 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)

6. Hi,

Please, don't say PDE... 'PDE' refers to partial differential equations, and this is a far different topic from partial derivatives !
It's really confusing if you don't talk about partial derivatives in your post... as it happened last time

7. ah ok, i just made the assumption that partial derivatives were used in the context of partial differential equations

8. Originally Posted by Noxide
ah ok, i just made the assumption that partial derivatives were used in the context of partial differential equations
Yes they are, but partial differential equations use more than just partial derivatives. There's a real gap between the two notions (I'd say that partial derivatives can be done as a freshman in university, but PDEs are rather at graduate level)

9. Originally Posted by Moo
Hi,

Please, don't say PDE... 'PDE' refers to partial differential equations, and this is a far different topic from partial derivatives !
It's really confusing if you don't talk about partial derivatives in your post... as it happened last time
Moreover, PDE = Partial Fraction Expansion.

**Edit**:
ohhh its D not F, xD.
Sorry!

10. Originally Posted by Noxide
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)
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!

11. Originally Posted by Moo
Yes they are, but partial differential equations use more than just partial derivatives. There's a real gap between the two notions (I'd say that partial derivatives can be done as a freshman in university, but PDEs are rather at graduate level)
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.