Question

Are integral curves and direction (slope) fields the same thing or is there a subtle difference between the two? Just asking out of curiosity.

Answer 1

an old book on calculus that I recommend http://finedrafts.com/files/CUNY/math/calculus/S%20Thompson/Calculus_Made_Easy_Thompson.pdf

Answer 2

Loosely speaking, you see `slope field` when you look at `flow of water` in a river or canal

`integral curve` is the `path` of a floating free body in that water current

Answer 3

the integral \(\int \) denotes the "sum of," so when we see \(\int dx \) we meant to say the sum of little bits of x

Answer 4

Is it correct to say "a specific path along water flow" is same as "flow of water" ?

Answer 5

semantically correct, @ganeshie8

Answer 6

@ganeshie8 I'd say so. lol

Answer 7

but just like anything in math, we need a preamble to make it comprehensible as such

Answer 8

I'm retaking differential equations and going over equilibrium solutions and classifying equilibria and I was just wondering what the difference was. I feel like the two terms are used interchangeably.