Vector Calculus: Path Independence
The line integral of the scalar field f ( x, y ) along a curve C ( x, y ) may be evaluated directly if both functions can be parametrized easily:
C
f ( x, y, z ) ds =
C
f ( x ( t ) , y ( t ) , z ( t ) ) x ' ( t ) + y ' (
Problem 4:
b' b
a' a
c
d
e
f
The compound is drawn as a line compound for simplicity, though a compound with off-stoichiometry can also be drawn. Some particular features to look for: lines a, a, b, b: These represent the two-phase equilibria between the