1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Vector Calculus

  1. Apr 17, 2004 #1
    Can anyone give me a very brief summary of what vector calculus means? I know this sounds like a "specify what you mean" type question, but I hope it isn't. Let me explain further. I know all the equations, how to find line integrals, what Green's theorem is, etc. but I don't exactly know what they mean (I have an idea but i'm just not as set with it as I am with single/multivariable calculus). When I find an integral with Green's theorem, what am I finding (generally)? What about line integrals (mass if you have a density if I recall correctly)?

    Also I have about 5-6 ways of writing what seems to be finding the same thing, ie the integral of F(r(t))*r'(t) = the integral of F*T ds (where * is dot product), etc. Are they just the same thing? Is independence of path just a special case of sorts for finding line integrals in vector fields?

    Any help is appreciated :smile:
  2. jcsd
  3. Apr 17, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    When people refer to just "calculus," they mean calculus on a single real function. When people talk about multi-variable calculus, they mean calculus on a single real function with several dependent variables. When people talk about vector calculus, they mean calculus on systems of equations described by vectors.

    For example, [itex]\vec F = m \vec a[/itex] is a vector equation, in which every vector is composed of three components. The vector equation is exactly equivalent to three independent real equations, [itex]F_x = m a_x, F_y = m a_y, F_z = m a_z[/itex].

    Vector calculus is calculus applied to vector equations, which are just systems of multiple real equations.

    - Warren
  4. Apr 18, 2004 #3
    Leading up to three higher dimensional versions of the fundamental thm of calc!

    Greens, Stokes and Divergence Thms ---
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Vector Calculus
  1. Vector calculus (Replies: 3)

  2. Vector calculus (Replies: 15)

  3. Vector calculus (Replies: 1)

  4. Vector calculus (Replies: 6)

  5. Vector calculus (Replies: 0)