Question on Function Notation

  • Thread starter Artimodes
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  • #1
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Main Question or Discussion Point

Hello everyone,

I'm a newcomer to this forum! I've been having particular difficulty lately with understanding function notation in higher level mathematics. I felt like it was a general post so I posted in the general math section. I've finished calculus 3 and am going to take engineering math (basically ODE and applications) next spring.

It is my understanding that for a three dimensional function, for example an elliptic paraboloid, it's written like:

f(x,y)= z =x2+y2

However, after looking at Paul's Online Notes on ODE here, he starts to describe Newton's Second Law as a differential equation. I knew that, but his notation threw me off:

eq0006MP.gif


Is force in this case a three dimensional function, due to force being a function of the derivative of velocity while velocity is a function of time? Just confused.

Thanks for any help
 

Answers and Replies

  • #2
Bacle2
Science Advisor
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I don't know if it is helpful to refer to the function as being 3-dimensional , or functions

being n-dimensional. Strictly speaking, the graph is 2-dimensional, but it lives

in 3-dimensional space. In the sense of F(t,v) , you can say that F depends on two

parameters, and, if you were to graph force using axes for t,v the (two-dimensional)

graph would live in 3-D.
 

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