In this class we will use Sage to graph and analyze multivariable functions. Sage is a free computer algebra system. You do not need to download Sage, it is available online at the Sage Cell Server. On this page, I will include a few examples of how to use Sage. I encourage you to use Sage on your homework.
The box below is a Sage Cell. Inside are instructions for the Sage Cell Server. Hit the evaluate button to see the output. Then, try to change the function f and see what happens to the graph when you hit evaluate again. Maybe try something more complicated like f(x) = sin(x^2).
In order to use Sage, you need to tell it which letters will represent variables. Sage always knows that x is a variable, so the line var('x') in the top example was redundant. However, it is not redundant in the bottom example. Try removing the first line from the example below, and look at the error you get when you hit evaluate.
Sage can work a calculator. Unlike a regular calculator, Sage tries to keep output in an exact form, it does not convert output to a decimal approximation unless you specifically tell it to using the float() function.
In the examples section of this website, I will post examples of how to use Sage to compute and graph most of the things we will encounter in this course.