Line integral from vector calculus over a closed curve

I present an example where I calculate the line integral of a given vector function over a closed curve.. In particular, I the vector function is a
$${\bf F}(x,y) := (-y/(x^2 + y^2), x/(x^2 + y^2)$$
and the closed curve is the unit circle, oriented in the anticlockwise direction.

I solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics.

Such an example is seen in second year university mathematics.

[DSnyd]

great accent, great handwriting, great teacher - better than my professor

[DrChrisTisdell]

@jsm666 The difference between path integrals and line integrals is the kind of F involved (scalar valued or vector valued). There is no distinction between the curves/paths of integration.

[DSnyd]

great accent, great handwriting, great teacher!! better than my university teacher

[AeonMelvsStar]

Please please please come and teach at UWA!! You're methods and teaching voice are second to none! :)

[Ensign_Cthulhu]

Here is what was confusing me.

For path integrals ON AN OPEN PATH it's int (F(c(t)) times magnitude (c'(t)).dt

For path integrals ROUND THE CLOSED CURVE it's int (F(c(t)) dot. c'(t).dt.

Have I got that right?

[DrChrisTisdell]

@jsm666 Do not worry. This is rather subtle and takes a while for the ideas to sink in!

[DrChrisTisdell]

Thanks for commenting and best wishes!

[tankintummy]

thanks, that explaination was done very well. My prof is too obsessed with electro-statics and his explainations are too abstract

[Ensign_Cthulhu]

@DrChrisTisdell *headdesk* Ah, crap. Shall go back to the books and try again. Thanks for that. :)