Parameters, Arguments, Variables, Constants I`m confused,

[wajed]

First of all,
I understand what a constant is, what a variable is, and somewhat what a Parameter is.

For parameters, as much as I know they are variables but of a specific type, for exmaple:-
a^2= B, where B is the area of the square..now "a" is a variable, but its also a parameter, since its of certain type...
I doubt I`m right, but that`s how a parameter is pictured in my mind, and I hope you correct it if its wrong.

For arguments, I totally don`t know what they are about; well, I read about them, but that turned out to be logic, and unrelated to the original topic (parameters, and parametric equations)



Since its hard to quote from a website, please visit: http://en.wikipedia.org/wiki/Parameter
and from the index you can go to:-
* 2.1 Mathematical functions
* 2.2 Analytic geometry

concerning * 2.1:

The two are often distinguished by being grouped separately in the list of arguments that the function takes

what are arguments? they seem to be everything that can be put in the function`s notation (like shown in the example: f(x1,x2,x3,x4...; a1,a2,a3,a4...)
BUT:

Strictly speaking, parameters are denoted by the symbols that are part of the function's definition, while arguments are the values that are supplied to the function when it is used. Thus, a parameter might be something like "the ratio of the cylinder's radius to its height", while the argument would be something like "2" or "0.1".

Now this is confusing! (If you can please clarify this to me?)
and as a result, and anyway.. I don`t get the whole thing!

what are parameters? how are they different than variables? and what are arguments?

In the special case of parametric equations the independent variables are called the parameters.

Now what I`m most concerned with is "parametric equations", so if this sentence means that I should skip all what I mentioned please tell me. (I`m totally confused and can`t judge right now)
What tells me that I shouldn't skip what I mentioned is that I`ve read the following - while I was reading on parametric equations, here is what I read:

In mathematics, parametric equations are a method of defining a curve using parameters. A simple kinematical example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion.

I don`t think this simply means "independent variables"!?

 

[slider142]

An argument is just a parameter or variable. If you have f(...), each item in between the parentheses, barring commas, is considered an argument.
Parameters and variables differ only in intent. For example, suppose you have a polynomial expression f(x) = ax² + bx + c that you consider a polynomial in x. You then want to consider the effects that varying the "constant" 'a' has on some property of the polynomial. Since f(x, a) is no longer a polynomial, you will instead want to consider 'a' a parameter of the polynomial f(x; a) and perhaps f(x; a, b, c).

 

[slider142]

Now what I`m most concerned with is "parametric equations", so if this sentence means that I should skip all what I mentioned please tell me. (I`m totally confused and can`t judge right now)
What tells me that I shouldn't skip what I mentioned is that I`ve read the following - while I was reading on parametric equations, here is what I read:

I don`t think this simply means "independent variables"!?

The parameter(s) in parametric equations aren't really related to the parameters in function specification. In this case, they are using parameter to mean an intrinsic variable, ie., suppose you have f(x) that represents the path of a particle where at each horizontal coordinate x, there is a corresponding vertical coordinate y corresponding to perhaps the height of the particle.
You may be more interested in the position of the particle as a function of time, so you want to know x(t) and y(t) from f(x). This is one way of parametrizing the curve with parameter t.
There are other parameters you may want to use instead; temperature, speed, arclength, or just an arbitrary mathematical parameter of your choosing.
As you go on, you will see that curves need one parameter and surfaces need two independent parameters, spaces need three to be specified and so forth, making the parametric representation of an object quite natural, like using natural internal coordinates, instead of trying to shove it into an arbitrary external coordinate system.

 

[wajed]

"An argument is just a parameter or variable. If you have f(...), each item in between the parentheses, barring commas, is considered an argument.
Parameters and variables differ only in intent. For example, suppose you have a polynomial expression f(x) = ax2 + bx + c that you consider a polynomial in x. You then want to consider the effects that varying the "constant" 'a' has on some property of the polynomial. Since f(x, a) is no longer a polynomial, you will instead want to consider 'a' a parameter of the polynomial f(x; a) and perhaps f(x; a, b, c)."

May I be bother you?
I don`t know why f(x, a) is not a polynomial
Can you please tell me what to read so that I understand this thing?
and Can you firstly give me a little explanation of why is f(x,a) not a polynomial? and why does using a parameter solve the issue?

 

[wajed]

oh, forget about the first and last question! now I got it!
I just misunderstood you when you mentioned "f(x, a)".. now I get what you mean..

but still my question is, how am I supposed to know the basics? how am I supposed to know this when I read my calculus book?! is there anything I need to read and start with (to begin from the scratch)?

 

[slider142]

Not really. Just keep asking critical questions and try to figure out the ramifications of things presented in the text before the text goes ahead and pushes them to you (pull info from the text instead of just having it pushed to you). A blackboard or other scratchpad is useful for this.