Level Curves of Functions of Two Variables

[sarahpanza]

This video is 9 years old and still so helpful, Thank you!!!

[randomguy_]

This is a 11 years old video, and still is one of the best ones for me as far as this topic is concerned,

[Brandoniafudgel]

Now, this channel is something I can get behind. The Pearson videos simply have no aura and reward rote memorization. Thanks for helping me with graphing, arguably one of my weaker skills.

[shlop]

Thank you sooo much ! This is just what I needed. 3D models really make it easier to visualize and understand !

[jonescomplete]

Your videos are my new favorite thing. Sending them to everyone that I know. Thank you so much. I hope to join you in online education in the future!

[akgh]

I'm studying at wake tech now and I've watched most of your amazing videos. Thank you so mutch.

[heidihuu]

I love youuuu, this is the only video that i found that actually explains how you find the x and y intercepts! Thank you

[Smiling_Tears]

Excellent! I am using the the textbook Calculus for Scientists and Engineers, and the authors' explanation of drawing level curves with an ellipse was fantastically terrible. Thank you for contributing!

[jr]

Thank you.

This is the first video that explained this in detail.
However, I am confused as to how the (a) and (b)'s you were getting out of the equations.

[ClownDatWalk]

this 10 min vid just taught me what i learned in lectures for a month

[Mikej]

@john Barre if I may try to answer, you are given two variables and finding the third. Z depends on X and Y so there are three variables, technically. The up or down depends on the function. Since they are x^2 and y^2 there can never be a negative Z because any number squared will be positive. so this will always go in positive z axis direction. if you are talking about the x^2+2y^2=z equation.

This video helped me understand so much about level curves in a single video, thank you good sir, hope you are doing well.

[mariaverde]

Thank you! All of your videos help me a lot​!

[m.m.]

James is an intelligent individual- THANK YOU!

[Mathispoweru]

@goddetective The standard form of an ellipse: x/a^2 + y/b^2 = 1 when centered at the origin.

[sagarmusicofficial]

Very nice explanation Sir. It is helpful for the Graduate students to understand the concept of the Level curves.

[waleedbintariq]

great effort, really appreciated for this video and especially for the quotation at the end

[BYEOLDAL]

This video is more helpful than my professor's 3 hrs lecture.

[dbskerrett]

Thank you so much.  How did you know it was an ellipse so quickly, and can you always find the a & b values by set the equation equal to 1 and square rooting the denominator?

[yifeiding]

thank you very much. This is helpful to me when reading the "convex optimization".

[johnbarre]

when creating the 3D graph from the level curve (the example problem you did of the elliptical parabola) how do you know which way the function extends (up or down)? because you're only given 2 variables... not 3.