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.

Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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