Question

please, can someone explain the concept of quadratic surfaces?!!!

Answer 1

Paraboloid, Hyperboloid, cone,cylinder are all quadratic surface

Answer 2

You do plane tracing to figure out the surface based on equation

Answer 3

been trying to figure them out. presently reading working some questions. but i'm totally lost. please, could you simplify what these surfaces are about.

Answer 4

@imranmeah91, what does plane tracing mean?

Answer 5

Example

f(x,y) = x^2 +y^2 is a paraboloid.

U can get it by rotating z = x^2 about the z-axis.

2D surface embedded in 3D.

Answer 6

x^2 + y^2 +z^2 =1
we want to know how the function look like in x-y plane, so we set the z equals to 0
x^2+y^2=1
so it is circle in x-y plane

Answer 7

lemme try to work on that for a minute...trying to relate that to what i'm reading frm the textbook...

Answer 8

I still don't understand.

Answer 9

Could you explain like from scratch?

Answer 10

This is now function of several variables rather than one.

Answer 11

ok...

Answer 12

So you have z = f(x,y) and the domain is R2

Answer 13

R2 means a rank of 2 right?

Answer 14

The plane, as opposed to the line of R1

Answer 15

k....

Answer 16

So now a surface is all points (x,y,z) = (x,y, f(x,y)) as x,y ranges over R2.

Answer 17

Essentially, you are just generalizing everything u know about stuff on the real line.

Answer 18

helps to draw lots of pictures...

Answer 19

better, use Wolfram to plot a bunch of 'em.

Answer 20

er...i'm not allowed to use wolfram in my exam

Answer 21

I know, I just mean to get familiar with it all...

Answer 22

i'll do that
but that'll be after the exams, which are pretty close right now. so, i kind of urgently need to learn how to draw them without wolfram, soon. please can you help me with that?

Answer 23

Then u r going to do derivatives on a surface with 2 vars instead of on a curve with 1, and so on...

Answer 24

I will be back after I eat something, let me think about a crash course in that.

Surfaces from conics might be a good place to start.

Answer 25

Thanks! :)

Answer 26

Hello?!!!!

Answer 27

I'm back now...

Answer 28

OK, probably the most useful thing to assist in visualizing these things is a section.

So say, we take the f(x,y) = x^2 + y^2 paraboloid which as I said above can be thought of as z=x^2 in(z,x) plane rotated about the z-axis.

Let's say we fix y at 2 then we have f(x,2) = x^2 + 4 which is like taking a knife through the surface and looking at the curve (1D) you get there.

With me up to here?

Answer 29

http://en.wikipedia.org/wiki/Quadric for some pretty pictures and standard forms.

Answer 30

http://www.wolframalpha.com/input/?i=plot+f%28x%2Cy%29+%3D+x^2+%2B+y^2

A plot in Wolfram.

Answer 31

Once u get the idea of how these surfaces work, you get to do (partial) derivatives (a plane tangent instead of a line, note that a plane is also a surface) and find minima/maxima and all the other stuff u do in 1D.

Answer 32

A good place to take sections is with something fixed at 0 as u might expect and will throw out many curves you are doubtless already familiar with.

Answer 33

ok..

Answer 34

back

Answer 35

checking the links

Answer 36

http://www.ucl.ac.uk/Mathematics/geomath/level2/pdiff/pd5.html

And this short explanation.

Answer 37

hello?

Answer 38

Go on..

Answer 39

thanks a great deal, i definitely still have a lot of studying to do on that. I really appreciate.

I've got to leave it be for now, i need to focus more on what i have a good grasp on for now then come back to quadrics after.

Answer 40

Please are you familiar with multiple integrals?

Answer 41

Sure but there are some calc wizkids out there much faster than me.

Put it up as another question.

Answer 42

thanks!

Answer 43

ur welcome.