[Multivariable Calculus] Level Sets of Real Valued Functions

In this video I go over the basics of level sets, which provide an alternative visual representation of functions through level curves and level surfaces. We look at a few examples of level curves and note the similarity between level curves and cross sections of a graph.

If you have any questions, feedback, or video requests, please leave a comment.

You can check out my multivariable calculus textbook here:

[dessalinesfrancois]

I am not sure why people have a hard time explaining things using plain English and concrete examples; thank you for this perfect explanation.

[What_a_piece_of_work_is_a_man]

Brilliant explanation!! the clearest I've heard on level sets, curves

[moss]

Great video, really helped me understand level sets

[krussell]

omg. I was struggling to understand why my teacher wrote a random variable representing a constant but this explanation of level curves is great!

[gulxar]

Good explanation abd example 👏 appreciated 👏

[mrbbayat]

Thanks for this nice and clear explanation.

[xyw]

Seems like the level set reduces the function dimension by one? I might misunderstood. If the actual function is more than 4 dimension, a level set representation is more than 3 dimension, which also cannot be drawn. What is the point of level set in that case?

[williambillemeyling]

What software/gadget do you use to draw on your screen like you do in this video?

[rakotondrazakatojoherilant]

f(x, y)= -x^2-y^2 draw the upper level set of the function for the value -1 ? ( can anyone help me with this )

[abuansari]

What about x^2+y^2 less than or equal to c

[mroliver]

you cannot pronounce the letter 'R' ?