Sections 9.1 and 9.2

Main Points: Section 9.1 talks about functions with two independent variables and states that the domain of a function f is a collection of all posssible inputs in (x,y). Also, the function is increasing if one variable increases while the other independent variable is held constant. This goes the same for decreasing functions. Contour functions can be represented numerically by a table of values, algebraicially by a formula, and pictorally by a contour diagram. A cross section of the function can be created by holding one variable fixed and letting the other variable change. Section 9.2 discusses contour diagrams more in depth. Types of contour diagrams include weather maps and topographical graphs. Contour graphs are made of curvy lines that show data, generally called contours. Weather maps have curves called isotherms which means "same temperature." Topographical graphs separate regions of lower elevation from regions of higher elevation. In this case, contours are also called level curves or level sets. The Cobb-Douglas Production model helps to figure out economic problems and has the standard form of: P=f(N,V)= cN^alpha * V^beta. In this formula, P is the total quantity produced, c, alpha, and beta are all positive constants, and both alpha and beta are greater than zero but less than one.

Challenges: The tables in section 9.1 really confused me. They were all really complex and I didn't really understand the examples at first. I understood the parts where the book gave equations, but looking at a picture got me really confused. In section 9.2, I wasn't really sure why they gave the Cobb-Douglas model and didn't do any sample problems with it. Also, the reasoning behind some of their explanations was worded oddly and I had to reread it to fully understand.

Reflections: These sections were totally new to me. I have never done these types of problems, but I like the fact that I can show increases and decreases in a picture. Sometime formulas are boring! Also, the section about topographical maps will help me understand those types of maps in classrooms better since before reading this, I wasn't really sure what they were for.