How do you sketch level curves of multivariable functions?
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- Опубліковано 4 жов 2024
- ► My Partial Derivatives course: www.kristaking...
In this video we're talking about how to sketch the level curves of a multivariable function.
Skip to section:
0:48 // What are level curves?
4:03 // How to sketch level curves?
5:02 // How to find equations of level curves?
7:52 // How to rewrite the function to graph the multivariable function?
12:15 // How many level curves should you draw?
13:30 // What are the level curves for a plane?
16:24 // Summary for how to sketch level curves
Whenever you're dealing with a multivariable function, the graph of that function will be a three-dimensional figure in space. If you take a perfectly horizontal sheet or plane that's parallel to the xy-plane, and you use that to slice through your three-dimensional figure, then what you get at the intersection of the figure and the plane is a two-dimensional curve.
What we want to be able to do is slice through the figure at all different heights in order to get what we call the "level curves" of a function. Then we want to be able to transfer all those two-dimensional curves into the two-dimensional plane, sketching those in the xy-plane.
This will give us the sketch of level curves of the function. In this video we're going to talk about how to find the level curves both graphically (by looking at a picture of the three-dimensional figure) and algebraically, by replacing z in the multivariable function with a constant c, and then substituting different values for c in order to get equations that are in terms of x and y only and can therefore be graphed in the xy-plane.
Music by Joakim Karud: / joakimkarud
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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WOW! You can not beat that handwriting! So c crisp and clear.
Thank you for sharing.
Dear Krista, I have faithfully watched yours and Christine Breiner’s (of MIT Courseware) Calculus videos. Truthfully, I am beyond amazed at both of your levels of skill and brilliance, and the ability to teach and do so in such a pleasant, down to earth, caring way. Thank you both for all you do and please continue with more videos. I am nowhere near your levels, but I do learn from you, and it is a very enjoyable learning experience each time. Blessings, George.
Thank you so much, George! I'm so happy that you enjoy the videos and are able to get great use out of them... I really appreciate you saying hi and letting me know! :)
@@kristakingmath Krista mam I also enjoyed 😊
Thank you, old guy going back to school needs all the help he can !
Good for you for going back, that's awesome! :)
Krista King just found out I can graduate in December, eye on the prize, son will graduate High school spring of 21’ just had to finish before he did
the best explanation I have ever seen
best explanation of level curves ever.
you right, calculator.
I can't believe i watched like 6 videos on this and NOBODY thought of putting the first diagram she put to the left (3 dimensional graph combining both the function and level curve), i've been trying to understand this for like 2 hours but one glance at the diagram made it clear
Best video I’ve found on this literally!!!! Thank you
Great video Krista King!
Thank you so much!! :)
It was very easy understand to with your explanation. Thank u very much.
You're very welcome, I'm glad it made sense! :)
Great video. Great drawings. Great Explanations. SO simple. Thank you
Been trying to search for this for 2 weeks. Finally understood. I remembered studying this in engineering some 13-14 years ago but I couldn't remember why the oval shape comes in and why it's slanted this way instead of that way.
Danke!
I love your videos! They helped me a lot through my calc 3 course.
Thank you so much, I'm so glad I could help! :)
Thank you! please, keep uploading more videos ))
Well-done, understood
omg !! the bestest video ever n
thanks 😊
this channel is the best
I hope you're happy about what you do.
Krista King, I gotta admit you are good, and very clear at your explanation. I watch a couple of your video, and now I can recognize the quadratic surface like drinking water as easy as peace of cake.
Oh good! I'm so glad the videos have been helping! :D
Thank you so much........... Best explanation. I was confused a lot before watching this video... Now the things are more clear to me
You're welcome, Manmeet! I'm so glad it helped! :D
This is so helpful! Love your clear explanation and voice!!!thank you
You're welcome, Jessica, I'm so glad this helped! :)
THANK YOU SO MUCH SHERA
You’re so welcome!! ❤️
Clear and great explanation ! thank you so much.
Thank you! I'm so glad it helped! :)
Thank you! That was great review.
Omg, your videos are absolutely great, thank you very much!
I'm so glad they're helping! 😊
Really nice video..... Easy to understand!!
Added to my education playlist. I only save the best on youtube. Thank you...and my future self who will also probably use this to relearn thanks you as well
I like you and like your video explaining the level curves
Your videos are amazing. Thank you so much!
Super explanation ...ma'am ..1👌👌
Thanks a lot, papa! :)
Great video!
Thanks, abdel! :)
Thanks for your amazing explanation!
You're welcome, Bowen, I'm so glad you liked it! :)
thank you
Helpful really!
Glad it was helpful, Unnati! :)
Extremely helpful!! Thank you!
You're welcome, Michael! I'm so glad it helped! :D
Best explanation with 4K video means I can skip the class and still get an A. Thank you so much
No problem, Prabin, glad it helped! 👍
that was great,loved your explanation,thank you.
It all makes sense now thanks a lot
omg you the best saved my life and time
I'm so glad it helped, amir! :)
Great video! well explained.
This is the first video I've ever seen offered at 4K/60fps
Thanks, very helpful to me.
You're welcome, Wahid! I'm so glad it helped! :)
Very helpful, thanks a lot!
best explanation ever I got
😘😘😘
i like your video. thanku😍
Thank you!
اعظم مدرسة ❤️❤️😘
Awesome...❤️
Life saver.💝
thank you 😍
👏👏👏Thank you alot
May I be so bold and ask what program/hardware you use to write these lessons? Thanks for the awesome content!!!
Hi Arno! I explain here: www.kristakingmath.com/blog/how-i-create-my-videos
thank you!
You're welcome! :)
great video ...just one thing...if you replace the C in the second example with a constant, then you are going to get a Hyperbola instead of an ellipse. but over all well explained. thank you.
Difficult concept with easiest way.....Thank a lot.
Can you sketch level curves of z=1/xy.
What if you dont realize the inherent curve of a function. Like knowing the equatuin of an eclipse for the second example? All these example on youtube are just for recognized equations
you are a gift from god
Perfect
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Awesome
Could you tell me please why the ellipsoid in the second example is elongated along the x-axis? The x^2 is divided by 4 but y^2 isn't, so I don't understand why x would be elongated. It seems to me that x would be shrunken more if divided by 4. Thanks.
with the ellipsoid equation, the denominator of x and y correspond to the 'magnitude' of the ellipsoid. meaning that, if you have (x^2 /a^2) + (y^/b^2), the size of the elipsoid will be: a (in x axis) and b (in y axis). In the example, x is divided by 4, (therefore the elongation will be in 2 **because root of 4 = 2** ), and y is divided by 1 (meaning its elongation in the y axis will be of 1). if you plot the points in the 2d graph, youll see that x is elongated
TE AMO
Hi thanks a lot for your amazing videos
If I want to study calculus 3 from your videos what is the order of the tutorial
Hey, Jake! Focus on Partial Derivatives first, then Multiple Integrals, then Vectors. :)
Numerology about Lahinch
Numerology (Expression Number), correct?
What program do you use for your sketches and videos? Its awesome!
Hey Alyssa! It's called Sketchbook. :)
God bless you
I love your voice!
May I know what apps do you use to do such things?
I use Sketchbook and Sceenflow, along with a Wacom pen tablet. :)
Can you please tell me which software are you using? It will really help me to teach the students in the class
It's called Sketchbook. If you want more information, here's how I put the videos together: www.kristakingmath.com/blog/how-i-create-my-videos
Okay, thanks a lot.
Thanks for it. Did you graph also in the sketchbook?
mam,can u post funcuntion video for beginers. ☺
How can i sketch the level curves when the question contains sin,cos,tan and others ?
Does anyone know the name of the software used in this video?
Hey, Zach! I use Sketchbook (by Autodesk) for the blackboard, with an old Bamboo tablet from Wacom, and then Screenflow to record and edit. :)
Nicely explained, just please label your axes :D especially in the 3D plots
Krista is clearly a goddess and we are lucky for her presence
Three-dimensional graph of z=x^2+y^2 is not correct
died at 9:10 lmaoooooo thank you
you look like sehnaz
Started wondering about orbits, gravity, and excuse me boobs
I wish I'd seen this before my first test >.
thank you