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Question on Function Notation

  1. Sep 2, 2012 #1
    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:


    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
  2. jcsd
  3. Sep 2, 2012 #2


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    Science Advisor

    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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