Data Analysis with Open Source Tools

Appendix B. Results from Calculus

IN THIS APPENDIX, WE REVIEW SOME OF THE RESULTS FROM CALCULUS THAT ARE EITHER NEEDED EXPLICITLY IN the main part of the book or are conceptually sufficiently important when doing data analysis and mathematical modeling that you should at least be aware that they exist.

Obviously, this appendix cannot replace a class (or two) in beginning and intermediate calculus, and this is also not the intent. Instead, this appendix should serve as a reminder of things that you probably know already. More importantly, the results are presented here in a slightly different context than usual. Calculus is generally taught with an eye toward the theoretical development—it has to be, because the intent is to teach the entire body of knowledge of calculus and therefore the theoretical development is most important. However, for applications you need a different sort of tricks (based on the same fundamental techniques, of course), and it generally takes years of experience to make out the tricks from the theory. This appendix assumes that you have seen the theory at least once, so I am just reminding you of it, but I want to emphasize those elementary techniques that are most useful in applications of the kind explained in this book.

This appendix is also intended as somewhat of a teaser: I have included some results that are particularly interesting, noteworthy, or fascinating as an invitation for further study.

The structure of this appendix is as follows:

1. To get a head ...