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Shadow12345
12-20-2002, 11:43 AM
from dictionary.com


a. A constant in an equation that varies in other equations of the same general form, especially such a constant in the equation of a curve or surface that can be varied to represent a family of curves or surfaces


What does this mean? If you are going to attempt to explain it to me keep in mind I am not taking calculus right now in school and have only barely started trig (meaning keep it simple if possible)

Thanks.

Davros
12-20-2002, 11:51 AM
Here's an example. I know you haven't done trig, but the following will give you a sine wave if plotted for differennt values of x. I'm hoping that you know what a sine wave looks like, but you don't need to understand it.

y = a * sin(f*x)

where x is the variable.

a & f can be considered constants, where a is the amplitude and f the frequency. However, if we change the value of f, it will give us curves of different frequencies (i.e. different members in a 'family' of sine waves). Therefore, a & f are parametrics.

Sang-drax
12-20-2002, 12:22 PM
Equations can be written on different form:

This is the normal form:

x/2 + y/3 = 5

Here is the solution to the equation on parametric form:

{ x = 2t
{ y = 15 - 3t

Where t is any real number

t is the parameter and for each different value of t, a new solution to the equation is obtained.

The solution to an equation can also have more than one parameter.

Shadow12345
12-20-2002, 12:22 PM
Actually sine and cosine waves is the total extent of trig that i have done and I have actually done my own little math programs in opengl doing 3d sine/cosine waves. Is frequency synonomous with wavelength?

and thanks for explaining that to me, it makes sense. changing a and f will still produce the same 'family' of models (sine waves) but they will be different in that the distance from crest to crest will change and the distance from the origin to crest/trough will change.

i was fooling with sine waves this morning
i tried having the amplitude start big then exponentiall go small and then the entire wave curves 'up'

y = (.5*.9^X) * sin(5X) + 1.1^X

Davros
12-20-2002, 12:39 PM
I think there's a slight confusion here, including my own. When I said, 'therefore a & f are parametrics', I think I was talking rubbish.

I double checked to parametric on dictionary.com - Shadow12345, your definition is for 'parameter', not parametric. The explaination I gave you applies to parameter, rather than 'parametric'.

Sang-drax
12-20-2002, 12:51 PM
Originally posted by Davros
I double checked to parametric on dictionary.com - Shadow12345, your definition is for 'parameter', not parametric. The explaination I gave you applies to parameter, rather than 'parametric'.

Yes, that makes more sense.

My explanation applies to the Swedish term "parametrisk" and I'm quite sure that the english translation would be "parametric".

golfinguy4
12-20-2002, 01:03 PM
Yep Sang, you got it right.

Shadow12345
12-20-2002, 01:06 PM
Ohhh so that means I gave the wrong definition, my bad! Well, now that I think about it, it wasn't to waste if you were still defining parameter because mathematically I didn't know what it was. So a parameter in math can kind of be considered like a parameter passed to a function in C++, the C++ function will still provide the same 'type' or 'family' of functionality but the actual results will change when different parameters are 'passed in' much like the amplitude and frequency of the wave will change based on different parameters 'passed in'. How sound is that logic?

I am still confused as to what parametric means, however


Here is the solution to the equation on parametric form:

{ x = 2t
{ y = 15 - 3t

are those curly braces necessary? As in do they mean anything specifically dealing with the 'parametric'? Can you find a definition of parametric? I couldn't because when I typed in parametric at dictionary.com it only came up with parameter. That sucks!

Want to know something else that sucks? The only way I can take calculus is if I take it as an extra math course :( The integrated math system I am in doesn't do calculus :(

golfinguy4
12-20-2002, 01:32 PM
Basically, in a parametric equation, x and y are set in terms of a 3rd variable t. When graphing, you choose the domain of t, and the interval. For example, say you have a car driving up a hill at 40 miles an hour. You can model it's position in terms of time, which will be t in this case. It's height will be in terms of t and so will it's horizontal position. However, since you only want to see the car's position for the first 3 minutes, you would set the domain of t from 0 to 3 minutes.

Davros
12-20-2002, 01:33 PM
>The only way I can take calculus is if I take it as an extra math course

I think it would be worth doing.

Shadow12345
12-20-2002, 01:45 PM
Thank you golfinguy that pretty much ties everything together. Thank you sand drax and davros for helping out.


I think it would be worth doing.


Well I asked my math teacher and he said that if I do well enough this year he would give me a recommendation to do pre calc next year on top of taking integrated math iv. I think that would look really good on my college resume thingamajobber. Do any you guys that actually understand all this math hype have trouble doing simple math problems in your head?
I swear I can't even add 16 + 82 in my head without a calculator. Actually now this brings me to a question I've been wanting to ask someone for a LONG time: How do you go about adding in your head? Lets say you are adding 16 and 82, I would do it like this:
add 80 + 10 to get 90
add 6 + 2 to get 8
add 90 + 8 to get 98

Do any of you go about doing it differently? I can't just look at it and instantly know it, it's like I have to reason with the problem and I actually say it in my head.

Eigenvalue
12-20-2002, 02:27 PM
<<Do any you guys that actually understand all this math hype have trouble doing simple math problems in your head?>>

:) I have problems like that all the time, and I just finished my Differential Equations class this past Monday!! ;)

The way I add 16 + 82 in my head is the same way you do. I think you should try to get into pre calc and all of the advanced math classes. If you have a solid understanding of algebra and trig anything else is alot easier to understand.:)

Eigenvalue

*ClownPimp*
12-20-2002, 09:45 PM
haha Eigenvalue, I just finished linear algebra this semester

Eigenvalue
12-21-2002, 06:34 PM
Originally posted by *ClownPimp*
haha Eigenvalue, I just finished linear algebra this semester

I had that last semester. It was alot of fun using matricies (sp). Our professor forgot that it was an introduction course and ended up teaching us the entire book (there were only four of us that signed up, it being the first time that they taught it at the community college). We didn't mind though.

Eigenvalue