Vectors and Vector Fields | Multivariable Calculus
In this video, we introduce the idea of a vector in detail with several examples. Then, we demonstrate the utility of vectors in defining vector-valued functions and vector fields. Finally, we wrap it up by showing why vectors and a vector fields are so fundamental to multivariable calculus: by moving towards gradients! Hope you enjoy!
Chapters:
0:00 Intro
1:07 What is Vector?
5:21 Vector-Valued Functions
8:14 Vector Fields
9:45 Vector Fields in Multivariable Calculus
10:58 Input Spaces
14:56 Gradients
18:58 Exercises
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Пікірлер: 4
Amazing video!! Just an insight to those taking multivariable calc this year(including me!!): a line integral is similar to a normal integral- when comparing the FToC to the FToLI, when you take a integral of small rate of changes, aka the derivative f'(x), it gives you the total change, f(b)-f(a). Similarly, in vector calculus, you can think of each vector in the field containing a weight, or a numeric value, at each point and thus the FToLI states that the integral of weighted rate of changes gives the total weighted length, which is the definition of a line integral! That's the way I like to view them. Anyways, can't wait for the next video!
No way I just watched your other calculus video earlier this week! Glad to see another upload!
great review😇
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