9.1 and 9.2

9.1 and 9.2.

1)Main points

This chapter has to do with functions that have two variables. All possible inputs ie; (x,y) is called the domain of f. By keeping one variable constant in a two variable function you can interpret useful data. For example, if you have an equation for the time of diffusion of a medicine in your body, you can keep the amount injected at a constant and notice the time it takes to diffuse, or you can keep the time constant and calculate the remaining medicine in the blood stream for a given injection. Two variable functions can also be modeled by a contour diagram (9.2). When depicting altitude on a contour map, the closer together the contour lines, the steeper the terrain. Also the numbers that label the lines usually stand for altitude on a topographical map.
In contour diagrams such as the corn example given in the book, information can also be collected by keep one of the variables constant and noticing how the effects of the other variable changing. The Cobb-Douglas function can be used to model economic output. A contour consists of all the points (x,y) where f(x,y) has a constant value, c.

2) Challenges

I find drawing contour lines very difficult. It is hard for me to find where the line should be from the data. In general thinking about a function with two variables is confusing, but I find it easier when I can use a real world example such as the office example about increasing staff & equipment. I will also have to remember which variable is which in a problem. For example, if there is a difference between the effects of rainfall than temperature on corn and it is easy to mix up those variables which would give some wrong info.

3) Reflections

Contour diagrams and two variable functions are used in all sorts of applications today. From maps to weather charts, and business or economic models. They model very real world situations and are extremely easy and quick to read. A map with contour lines can show you the altitude and shape of a mountain in an incredibly useful way.