Algebra 18 - Multivariable Functions

Although many familiar functions process a single input variable to produce a single output value, multivariable functions can be created whose output depends upon multiple input variables.

[vaishnavchandra]

The clean visuals make the concept very intuitive

[adastra]

❤❤❤❤❤ Thank you.
This is the only video so far out of the ten or more I have watched that explain the basics of domain and range so simply.
Brilliant 👏 👏 👏 👏.

Subscribed straight away.

[MusIsWorld]

Just as expected .. Entertaining and informative video .. Thnx a lot guys and I sincerely hope the lack of millions of views like a bieber video do not discourage from making more of this awesomeness

[arifkizilay]

Math is the most abstract type of knowledge. Thank you again for this wonderful lecture.

[dr.cherylavila]

Where were you when I was taking Calculus 2? Oh, that's right, they didn't have WhyU then, or the internet, or cell phones for that matter... "The kids today have it so good" and for understanding the concepts behind the procedures, you make understanding fun! I am one of your biggest fans. Keep up the good work.

[AnalyticMinded]

This is awesome! Mathematics can be so beautiful.

[rinostik]

Well made as usual, keep the great work up!!

[azizghalib]

Functions of two variables vs linear equations of two variables: Are they really different in their graphs? One produces a surface and the other gives a line. Also an equation in three variables gives a plane! What is going on here?

[FreddieF]

Is the Cartesian product the same as a union?

[pauluk]

5:14 "maps points in a plane to points on a line". This threw me because I was thinking of the output of the function as a surface. But that description is accurate by considering just the 'projections' of function values onto the z-axis. It's only when all three variables (2 input and 1 output) are combined into a 'graph' that we get a 'surface' (that is part 'input' and par 'output')

[GHXL]

I apologize but what does "Mathematical Properties" mean? I usually hear that yet do not really grasp the meaning. Apologize as I am not mathematician. I only study it by myself.