## 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.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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