Problems for Chap

6.1 Consider the following total differentials:

dw = y(3x2 + y2)dx + x(x2 + 2y2)dy and dz = y(3x2 + y)dx + x(x2 + 2y)dy

For each, determine:

(a) Whether either or both is exact in the sense of Eq (6.4)

(b) Whether either or both is exact in the sense of Eq (6.5). Test this condition by integrating over two paths: Path A: y = F(x) = x and Path B: y = F(x) = x2. The initial and final states are x = 0 and x = 1.

(c) If either total differential satisfies the (a) and (b) exactness conditions (to be exact, it must satisfy both), determine the function w(x,y) and/or z(x,y) from which the total differentials arise.

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