section 9.1 & 9.2

Main Points
The functions of two variables described in this section have two independent variables which affect the dependent variable instead of just one independent. A table of values can be used to demonstrate the function or an algebraic function itself can be used. If you want to see how the variables affect the dependent variable independently (though it's not that useful in every situation), you can define one of the variables to see how that affects the function. Contour diagrams are one graphical way to show information from a two variable function. Contour diagrams show equal values of the function connected by lines. This helps to visualize the idea. Cobb and Douglas came up with a two variable function for worker productivity and capital investment. P= f(N,V)=cN^aV^b. Contours on the diagrams are found by setting the dependent variable equal to a value and then plotting the resulting line equation.

Challenges
The whole setting one variable equal to something and then graphing the two variable function is confusing for me. I would like to see/do an example of isolating one variable in class. I'm pretty sure it's easier than I think, but the two graphs the book shows are slightly confusing.

Reflections
I thought the contour mapping section was really interesting. I never considered that those temperature maps were just lines connecting places with a temp on a ten degree interval.