Changing tides (the prodigal returns)

There's a reason I started this project over the summer... now that I'm back teaching, there are so many urgent tasks to complete that blogging can fall to the side! I'm used to making a point of carving out time for research: on a personal level, I don't feel like a vital mathematician or teacher if I'm not creating mathematics. I have less practice, though, making time for math communication outside the classroom.

How are your semesters going? It is that time when you might feel that the semester's been going on forever, and yet the end is not near. We all know the end is rushing toward us, though, and it's the time when we try to remind students who might have been slacking or who have started getting discouraged that we have almost two months to wrestle a class into success or let it sink into failure.

In my calculus class right now we're dealing with derivatives of arcsine and arccosine, but I am not going to talk about those today. Instead I'll put up the natural follow-up to the last post, a spreadsheet worksheet on modeling ocean water level over 24 hours.

On a short timescale, tidal changes really can be modeled pretty well by a simple sine function. As you work through the following, you'll see how well it works. However, over longer timescales much more complicated formulas are necessary. Check out this set of AMS articles for information about using Fourier analysis to get a better understanding of tides, as well as some musical "audializations" (?!) of tidal data. Another good resource for further learning is from Data in the Classroom -- their site on sea levels has multidisciplinary resources for exploring the data.

Our worksheet is a condensed version of the functions worksheet, augmented with questions about rate of change:

Derivatives: Modeling Tides

Here's the link to the Google spreadsheet of sea level data from Point Reyes, California, formatted for the worksheet:

Google spreadsheet of data

Of course, if you want to reproduce an activity like this with data from some other location, check out NOAA's tides and currents pages! And sign up for the mailing list to get solutions 🙂

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