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Course: Multivariable calculus>Unit 1

Lesson 1: Introduction to multivariable calculus

Multivariable functions

An introduction to multivariable functions, and a welcome to the multivariable calculus content as a whole. Created by Grant Sanderson.

Want to join the conversation?

• Is learning ahead good? Because i am only in 8th grade.
• It is all about the prerequisite. If you have master the "single variable" calculus, then you can give it a go.
• Can Multivariable functions be the functions?
The definition of function is that "one input - function - one output". But Mutilvariable functions have multiple inputs and multiple outputs.
I can't understand why people call this function.
• If your function has two real-valued variables, view the domain as a set of ordered pairs. If there are no restrictions on the domain you can think of every point on the x-y plane as a unique input. After all, couldn't f(1, 2) and f(1,3) be different?
If your function has three variables, view the domain as a set of ordered triplets. Then you might imagine points in space as being the domain.
Once you get more than 3 variables the idea is the same. So for a 5-variable function the members of the domain are ordered 5-tuples and look like this: [x1, x2, x3, x4, x5] It just becomes harder to imagine these "points" as a physical entity.
• 3Blue1brown
• How can I do animations like these? Any particular language/library?
• You might check the Github page for 3Blue1Brown, where he has a python library he uses for his videos called `manim` (he teaches this course as well). https://github.com/3b1b/manim
• What is the highest math you can do? Like when does it stop?
• Ultimavariable Calculus.
• what are the prerequisites for this course ?
• And of course an inquisitive (curious) mind, but you seem to have that already. It would be nice to hear if you ever finished the course.
• Beginning at around as Grant alludes to multivariate functions as transformations of a given input space--is there a proper name for that sort of animated visualization? In other words, how would a user's manual for a piece of plotting software refer to that particular feature?
• Linear Algebra is the study of how functions (which are codified by matrices) transform R^n into R^m for some n and m. You can look into that for details.