12.6: Cylinders & Quadric Surfaces

Objective:
33. Sketch the standard quadric surfaces and the graphs of certain cylinders.

[@alexquahzhiwei]

Thank you so much Prof Alex!! Was having a really hard time understanding my university professor as he cramped the whole chapter into a 40 minute video. It was really helpful that you have broken the chapter down into smaller topics and giving examples for us to understand clearly! Thank you so much again for your help with this topic! - Student from Singapore.

[@thomasfowler1]

You got me through 2nd year Calculus last year. Thank you for your coverage of James Stewart's Calculus book! Literally a life saver

[@beetlejuice2725]

Very helpful. My calc 4 professor barely covered conic sections and my precal professors NEVER introduced it to us whatsoever. Needless to say, this is gonna help me tremendously on my midterm tomorrow!

[@lorax121323]

What's Calculus 4? I thought Calculus 3 (Multivariable Calculus) was almost always the last course in the calculus sequence.

[@suckmyhugewiener633]

Calc 4 hell naw

[@teodorilie2049]

IT engineer student here, it really helped me. Thanks :)

[@BabaSphere]

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[@zasss4423]

oh my god! THANK YOU SO MUCH Prof Niedden!!! You literally saved my life! My Calc3 teacher used just 20 minutes with this topic and he taught me nothing! After just listening for 10 minutes, I understood everything! I will keep listening to your course for the rest of the semester!

[@nabankar]

lol my teacher took an hour but still it was awful..which college have you taken admission in btw?

[@andream8671]

Thank you so much!!! I’ve been struggling with these concepts in my Cal 3 class, but It’s easier to understand now. Thank you!

[@wolfyngrey1313]

Thank you! This has been the worst in cal3 thus far

[@oliviareul2387]

Thank you so much for these videos. You explain these concepts better than my professor.

[@abdullahe3674]

Bless You Dear Professor ,Math Wizard :) underated free content xoxo

[@d0l__meng__]

Thank you professor You’re drawing is perfect fr

[@duyquangbui5297]

Your lectures are very easy to understand, thank you so much for your lecture. It's very helpful

[@ansnaeem.7564]

Your way of speaking is good.

[@monbebeminmoongie9409]

The most helpful video about this topic. Thank you

[@nameenjunaidi445]

I am watching this before my classes so I can understand better my classes

[@lucasfc4587]

This has been great as an explanation and summary

[@shinkansen1907]

Thank you so much! love from Bogazici University!

[@scumble8271]

this helped a lot to help me prep for my exam thank you !

[@abdulwahed1803]

you made it easy to understand , thank you

[@user-ww2qs3cj9n]

Thank you so much for explaining it a million times better than my home university professor. A thanks from Seoul, South Korea. Btw, if I may ask, what is the pen you are using it sounds so nice!

[@denisesoto1175]

How are you finding the intercepts? Specifically for example #5?

[@alexandraniedden5337]

Substitute 0 for two of the variables. For example, for the x-intercept(s) in #5, set y=0 and z=0. You then have -x^2/a^2 = 1. This equation only has imaginary solutions so there are no x-intercepts.

[@isaachiew4906]

@@alexandraniedden5337 Hi there Prof, does that mean there is no z-intercept for general shape 4 and that it only has an imaginary z-intercept?

[@alexandraniedden5337]

@@isaachiew4906 There is no z-intercept for shape 4 in this form. That being said, the equation could be altered like the following: x^2/a^2 + z^2/b^2 - y^2/c^2 = 1. In this case, the hyperboloid would be drawn around the y-axis, so there would be no y-intercepts.

[@hermanfourie66]

Thank you very much for your help! This helped me a lot!

[@johnmarkbarinos6873]

PLS CREATE MORE CAL 3 VIDEOS. THANK YOU!

[@James15412]

you saved my life! thank you!

[@adilrhyder]

Thank you so much! Got a quiz in half an hour lol

[@user-qe4vw5gm7i]

Thank you Professor

[@haseebkhan4027]

Thanks you ma'am

[@juksjunior1136]

wow yoh perfect explanation first 3 minutes i was already Saved

[@fortunatenkuthalo]

thank you

[@mydawit]

In 3D space having only 2 variables in the equation for a Cylinder is necessary but not sufficient. For instance z=x^2 (as shown in the video clip) is a parabolic cylinder sitting on the y-axis. z= x^2 + y is also the same cylinder tilted and sitting on the z=y line. But 3 variables are present. Just a question for thought. Can we categorize a Plane to be a Cylinder? It sure does satisfy the definition of a Cylinder

[@ismailsurnameless178]

the noise of the pen is disturbing

[@kunalrout45]

Thank you professor this was sooooo helpful...

[@ifeanyiogbennaya7773]

for no.5 your intercepts confuses me. do we make (y-1)=0 for intercepts or do we make only y =0?

[@albert_ma4021]

thanks

[@samiullahsaddique8919]

Why in question 5 the third intercept is not possible?

[@saikartheek9707]

@alexandra budden Another doubt. In the 3rd general shape i.e elliptical paraboloid, why is there no paraboloid on the -ve direction of the z-axis. Sry for repeatedly asking u.😅

[@alexandraniedden5337]

No need to apologize. The elliptic paraboloid does not extend to negative z because of the restrictions in the equation. Z is equal to the sum of x^2 and y^2, so z will never be negative (z is the sum of two positive quantities). This is why the figure does not extend where z < 0.

[@saikartheek9707]

@@alexandraniedden5337 thanks a lot.

[@computerwebtraining.alirez4370]

Very good.😊how can lean draw p=cos€ in spherical coordination?

[@simba6964]

What textbook was that?

[@carlosmejia2284]

Debe ponerle las letras de las variables x y z a los ejes, porque no lo hace, debe ser estricto en ese sentido

[@9LimaAlpha7]

is there a followup video to this one, where you solve more exercises?

[@mdtarekulislam2440]

Take love mam...❤❤❤

[@BWAYOERIA]

👍👍

[@sarthakgaba1583]

Thanks😀

[@Mary-mj7le]

for hyperbolic paraboloids i have to find the saddle point :(

[@mashrafihaider7595]

For Ex #4 when you are finding the traces you said when y=1 then x=1 and z=2. Can you please explain how? @Alexandra

[@alexandraniedden5337]

I chose a few values for x, y, and z to investigate the patterns for the traces. For example, as y increases, each trace will be an ellipse. I hope this helps!

[@simba6964]

@22:29 what book is that please?

[@alexandraniedden5337]

Stewart's 8th edition Multivariable Calculus

[@simba6964]

@@alexandraniedden5337 thanks

[@ansnaeem.7564]

Plz make a video about 3d transformation system.

[@saikartheek9707]

what is the z - intercept of the 4th general figure. @alexandra budden

[@alexandraniedden5337]

In the example I gave, there are no z-intercepts. If you substitute x = 0 and y = 0 and solve for z, you will get z^2 = -c^2, which has no real solutions.

[@saikartheek9707]

@@alexandraniedden5337 thanks a lot.

[@taqqiraja2722]

21:55 lmao tanktop

[@aviationenthusiast4353]

In example 5, how did you find the center of the ellipsoid? how do you find the center in general?

[@alexandraniedden5337]

I found the center by completing the square. In this case, I needed to complete the square for both y and z.

[@ilkeuyankerstudent5347]

At 28:21 why did not look xy trace? Can someone explain?

[@alexandraniedden5337]

I did not look at the xy-traces because I could already see the shape of the graph with the information I had. That being said, you can certainly investigate the xy-traces. In this case, they are similar to the yz-traces - they will be lines.

[@ilkeuyankerstudent5347]

@@alexandraniedden5337 Thank you so much. I can not think 3D.. So it will be the same shape since it is 3D right? Thanks again :)

[@alexandraniedden5337]

@@ilkeuyankerstudent5347 I'm not quite sure what you mean by "same shape." The xy- and yz- traces are similar in that both contain sets of lines. There will be sets of "x"'s in the yz-plane and also sets of "x"'s in the xy-plane, giving that cone shape. It can certainly be hard to visualize!

[@ilkeuyankerstudent5347]

@@alexandraniedden5337 Okay I think I understood. Thanks a lot for your answers :)

[@abdullahmurtaza7155]

Mam wana talk to u

[@ramizhossain9082]

Easy

[@nevilholmes5900]

thanks