Coordinate Systems and a Tour of \(\displaystyle 3\)-Space
The graph of a function of a single variable is represented in \(\displaystyle 2 \)-dimensional space, with one axis (usually the \(\displaystyle x \)-axis) giving values of the independent variable, and the other axis (usually the \(\displaystyle y \)-axis) giving values of the dependent variable. In multivariable calculus, we consider functions of two or more variables. Accordingly, to visualize their graphs, we need to work in higher dimensional spaces — for example, the graph of a function of two variables is represented in \(\displaystyle 3 \)-dimensional space, with two axes (usually the \(\displaystyle x \)-axis and \(\displaystyle y \)-axis) giving values of the independent variables, and the other axis (usually the \(\displaystyle z \)-axis) giving values of the dependent variable.
This worksheet provides a basic introduction to \(\displaystyle 3 \)-dimensional space, including how to graph equations and inequalities. There is also an introduction to the different coordinate systems that will be used throughout the course.