Determining Independent and Dependent Variables in Calculus

[crono_]

Calculus is quite new to me, so I think I'm starting from scratch and might be in over my head. Forgive my basic knowledge...

When considering two variables, how does one know which one is the independent or dependent variable?

For instance - The area A of a circle depends on the radius r of the circle.

Okay, it clearly states that A is dependent on r. But can you not also say that r is dependent on A?

If you have a bigger radius then you'll have a bigger area. But vice versa, if you have a bigger area than then don't you automatically get a bigger radius? Doesn't this mean that they can both be considered the dependent or independent variable depending on how you view the question?

Thank you!

 

[tiny-tim]

Hi crono_!

When considering two variables, how does one know which one is the independent or dependent variable?
…
Doesn't this mean that they can both be considered the dependent or independent variable depending on how you view the question?

Yes!

You'll find soon that if y is a function of x, then you can differentiate and get dy/dx, but that's also 1/(dx/dy), the derivative of x as a function of y.

(btw, I'm not sure where you got "independent" or "dependent" from, for one variable … there's not much point in a variable unless something depends on it, is there? … of course, if there's two or more variables, they can be independent or dependent of each other)

 

[crono_]

Okay, thanks. That kind of helps to clear things up. Though I'm going to have to adjust to using calculus lingo. :)

The dependent & independent terms came from the textbook:

A symbol that represents an arbitrary number in the domain of a function f is called an independent variable.

A symbol that represents a number in the range of f is called a dependent variable.

That sort of seems straightforward, but my brain tells me that, depending on how you interpret the question, either of the two given variables could be dependent or independent.

The cost C of mailing a first-class letter depends on the weight w of the letter.

So, given the weight you can determine the cost. But, coming from the other direction, if you're given the cost then you can use that to determine the weight.

This is going to be a long term!

 

[tiny-tim]

The dependent & independent terms came from the textbook:

A symbol that represents an arbitrary number in the domain of a function f is called an independent variable.

A symbol that represents a number in the range of f is called a dependent variable.

Must say, that seems a bit daft to me.

And pointless.

oh well …

 

[crono_]

Must say, that seems a bit daft to me.

And pointless.

oh well …

Comforting. haha :P

Well, thanks for the comments anyways. They're appreciated, and comical! :)