Calculus On Your Own

In order for you to step out of this book and start doing calculus on your own, the first step is to construct a functional mathematical model of your data. Geogebra has a powerful toolkit for constructing single variable functional models. We used it multiple times in this book to construct the models of the height of the incoming missile, the length of the day in Johnson Vermont, the rate of traffic on Route 15 in Johnson Vermont, and the user headcount of Instagram. As you'll see if you go back and review those four activities, I progressively made you more autonomous. In the first activity where you modeled the height of the incoming missile, I only asked you to select the regression model (polynomial of order 2, AKA a quadratic), and then in later exercises I pushed you a little harder and had you do more of the task by yourself. For instance when you built the model of the length of the day in Johnson Vermont I asked you to highlight the data and open the Two Variable Regression Analysis Tool on your own. The only skill you need now to "close the loop" and be fully autonomous is for you to understand how to get bivariate data into Geogebra. This is a straightforward procedural task that is no harder than any other office computer task you are likely to encounter at work.
  1. (Hardest step) Your bi-variate data must be formatted so that it is stored in two columns. The term "bi-variate" means that each row of your two-column data set must represent a pair of values of an independent variable and an associated dependent variable. For instance, the first column could be time, and the second column could be height as in the incoming missile activity. If this doesn't make sense to you, go back to the examples listed above and see how each model started from a bi-variate data set that was in just such a two column format. The best software to use to store and format your data is something like Microsoft Excel, Google Spreadsheets, or Open Office. Any spreadsheet software is fine.
  2. Open the Spreadsheet View in Geogebra. You can read more about the view here. In general, the Spreadsheet View of Geogebra can be thought of just like any other spreadsheet, except each cell can be thought of as its own little input bar. In this way the Spreadsheet View deeply integrates with Geogebra. So if you store a number in a cell, the number won't show up in the Graphics View since number objects aren't plotted, but if you store a point such as (1,2), that will show up in the Graphics View.
  3. Copy and paste your bi-variate data columns from Excel or comparable into the spreadsheet view of Geogebra. Tidy it as you would in any other spreadsheet software. If you run into any troubles with the copy and paste, I recommend saving your data in ".CSV" in your spreadsheet software first, and closing the program, re-opening it, and then trying again. The format ".CSV" stands for comma separated values, and is kind of like the least-common-denominator data format of all spreadsheet and database software.
  4. Proceed as you did in any of the modeling applications we did in this course (see the links above in the header paragraph for examples) to construct your model.
This is neither time nor the place to discuss model type selection or testing. That is an entire other course. That said, there's nothing to stop you from using the Two Variable Regression Analysis tool now to begin exploring. In the near future I will be writing a few example activities to illustrate this process. They will appear below. Once you have a mathematical model from Geogebra, you can then use what you've learned to do a derivative-analysis of it to find the model's predictions of maximums and minimums of the dependent variable. If the model is of a rate of some physical quantity, you can use the integral to see the accumulated effect of the rate. As noted, additional examples of this process will be added to this chapter in the future and listed here as they become available. Here are those that are currently available: **NONE YET AS OF AUGUST 8, 2019**