✔ 最佳答案
(1). Integration on a closed loop (在閉曲線上作積分)
(2). This is very difficult. A differential dQ is exact if the function Q exists and the value of Q is independent to the path we took for the path integral for dQ.
This means that the integration in (1) over a simply connected domain is always ZERO if dQ is an exact differential.
e.g. dQ=Qy dx + Qx dy = (1 + (y/x)^2)dx - 2(y/x)dy is an exact differential since Qyx = Qxy. We have Q(x,y) =x -(y^2 /x) +K where K is a constant and x>0 . Note that the domain x>0 is simply connected.
e.g. dQ= Qy dx + Qx dy =(x^2 + y^2)dx - 2xydy since Qyx is not equal to Qxy
2006-12-31 09:33:43 補充：
SORRYe.g. dQ=Qx dx + Qy dy =.....e.g. dQ= A dx + B dy =(x^2 + y^2)dx - 2xydy since Ay is not equal to Bx
2006-12-31 18:21:00 補充：
The integration of an exact differential dQ is usually referred as the workdone by an object against a potential field Q, such as gravitational field. This is just equal to the difference in potential energy from final position to initial position.
2006-12-31 18:22:34 補充：
A potential field is usually viewed as a " contour map " or " isotherm diagram " .
2006-12-31 18:23:45 補充：
I don't know much about thermal physics. I am sorry that I cannot help you further.
