It's tough to tell precisely what you're after. Perhaps you could give an example of what you're looking for.
My first response is to recommend that you look into R http://www.r-project.org/ and some of the GUIs based on it. It's quickly becoming a standard in any field requiring statistical analysis, from quantitative finance, to medicine, to social sciences.
It has a hideous programming language but a huge package archive http://cran.r-project.org/. I would recommend poking around the statistics stack exchange site for pointers, but some notable GUIs include RapidMiner (http://rapid-i.com/content/view/181/190/), RStudio (New and just getting out of the gate, so don't expect a lot right now http://www.rstudio.org/), Red-R (http://www.red-r.org/), R Commander (http://socserv.mcmaster.ca/jfox/Misc/Rcmdr/), and Rattle (http://rattle.togaware.com/). R is also integrated in SAGE, with which you may already be familiar. One huge benefit of R is Sweave, which allows integration with LaTeX, so your papers can render your data and publication at the same time.
If you just want a graphing solution, WaveMetrics IGOR (http://www.wavemetrics.com/) is probably the best bet. It's available on Windows and Mac OS so you can share files with other people fairly easily.
KaleidaGraph (http://www.synergy.com/) and pro Fit (http://www.quansoft.com/) are notable options as well.
One of the secrets you'll find out when hanging out on various visualization forums, especially Edward Tufte's (http://www.edwardtufte.com/bboard/q-and-a?topic_id=1), is that a large number of the published graphs (especially his) often start in Excel and are exported to be manipulated in Adobe Illustrator. You may have a graph in mind that comes from this pipeline, which has a large manual effort but a magnificent potential output. I've also done similar with Mathematica (my tool of choice) when needing print-quality output.
First select both equations in the sidebar, and then Equation » Integration… in the menu.
In the dialog, it has preselected Area Between Curves. Confirm it.
You can change the color in the inspector window.
Since your second equation is y=0
, you could just select the first one, and integrate it, selecting Area in the dialog. The result should look the same.
Best Answer
Yes, indeed it can:
Square wave: try something like
y = (-1)^round(x)
(but with proper formatting). Something likey = (round(x+0.5) - round(x)) - 0.5
would also work.Sawtooth wave: try something like
y = x mod 1
or, more elaborately,y = 2((x-0.5) mod 1) - 1
. However, something likey = x - round(x)
would also work. If you don't like any of these, try something likey = x - floor(x)
.The triangular wave is left as an exercise to the reader ;-)
Of course, you can also use the truncated Fourier series, but that may be too wiggly for your taste.