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.
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!
I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU IVE NEVER CRIED TEARS OF JOY IN MY LIFE YOU SAVED ME FROM DROPPING OUT LEGITIMATELY CUZ I COULDNT AFFORD TO RETAKE THE COURSE AND GOT NO AID BUT YOU SAVED ME AND FOR THAT IM FOREVER GRATEFUL I LOVE YOU SO MUCH
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!
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!
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 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.
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
@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.😅
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.
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!
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.
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 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!
![Eminem - Somebody Save Me (feat. Jelly Roll) [Official Music Video]](http://i.ytimg.com/vi/Vwa0HenQMi4/mqdefault.jpg)
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.
You got me through 2nd year Calculus last year. Thank you for your coverage of James Stewart's Calculus book! Literally a life saver
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!
What's Calculus 4? I thought Calculus 3 (Multivariable Calculus) was almost always the last course in the calculus sequence.
Calc 4 hell naw
IT engineer student here, it really helped me. Thanks :)
I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU IVE NEVER CRIED TEARS OF JOY IN MY LIFE YOU SAVED ME FROM DROPPING OUT LEGITIMATELY CUZ I COULDNT AFFORD TO RETAKE THE COURSE AND GOT NO AID BUT YOU SAVED ME AND FOR THAT IM FOREVER GRATEFUL I LOVE YOU SO MUCH
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!
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!
lol my teacher took an hour but still it was awful..which college have you taken admission in btw?
Thank you so much for these videos. You explain these concepts better than my professor.
Bless You Dear Professor ,Math Wizard :)
underated free content
xoxo
Thank you! This has been the worst in cal3 thus far
Thank you professor You’re drawing is perfect fr
Your lectures are very easy to understand, thank you so much for your lecture. It's very helpful
Your way of speaking is good.
The most helpful video about this topic. Thank you
this helped a lot to help me prep for my exam thank you !
This has been great as an explanation and summary
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!
How are you finding the intercepts? Specifically for example #5?
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.
@@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?
@@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.
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
Thank you so much! love from Bogazici University!
I am watching this before my classes so I can understand better my classes
PLS CREATE MORE CAL 3 VIDEOS. THANK YOU!
you made it easy to understand , thank you
What textbook was that?
wow yoh perfect explanation first 3 minutes i was already Saved
Thank you so much! Got a quiz in half an hour lol
Very good.😊how can lean draw p=cos€ in spherical coordination?
you saved my life! thank you!
Thank you Professor
is there a followup video to this one, where you solve more exercises?
Why in question 5 the third intercept is not possible?
thank you
Thank you very much for your help! This helped me a lot!
for no.5 your intercepts confuses me. do we make (y-1)=0 for intercepts or do we make only y =0?
the noise of the pen is disturbing
Thanks you ma'am
Thank you professor this was sooooo helpful...
@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.😅
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.
@@alexandraniedden5337 thanks a lot.
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
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!
thanks
Debe ponerle las letras de las variables x y z a los ejes, porque no lo hace, debe ser estricto en ese sentido
@22:29 what book is that please?
Stewart's 8th edition Multivariable Calculus
@@alexandraniedden5337 thanks
what is the z - intercept of the 4th general figure. @alexandra budden
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.
@@alexandraniedden5337 thanks a lot.
Plz make a video about 3d transformation system.
for hyperbolic paraboloids i have to find the saddle point :(
Thanks😀
👍👍
In example 5, how did you find the center of the ellipsoid? how do you find the center in general?
I found the center by completing the square. In this case, I needed to complete the square for both y and z.
At 28:21 why did not look xy trace? Can someone explain?
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.
@@alexandraniedden5337 Thank you so much. I can not think 3D.. So it will be the same shape since it is 3D right? Thanks again :)
@@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!
@@alexandraniedden5337 Okay I think I understood. Thanks a lot for your answers :)
Take love mam...❤❤❤
Mam wana talk to u
21:55 lmao tanktop
Easy
thanks