MATH 211 Useful Links

Useful Links

I will add links to this page as the semester progresses. If you find a site that you think should be included, let me know and (if I agree!) I will put it up.


Generally Useful Tools

  • We will be using the Desmos online graphing calculator frequently throughout the semester. Feel free to experiment with it. There are a lot of interesting and useful demos on the site (take a look at their art gallery, all produced by students, some time!), but you can also experiment with making up your own examples, or using it to help make sense of homework problems from the textbook.
  • I mentioned Wolfram Alpha in class. This is an all-purpose online calculator, but it will in particular graph functions and compute derivatives. To compute the derivative \frac{d}{dx}(x^4 - x^2), for example, enter “diff(x^4 – x^2, x)”. (Without the quotes.)
  • Here is a slightly simpler Derivative Calculator. This one graphs both the function and the derivative on the same graph.

Definition of the Integral (Riemann Sums)


Definition of the Derivative (Instantaneous Rate of Change)


Average Rates of Change

  • A Desmos page in which you can manipulate secant lines to see what happens as the variable point on the graph approaches the fixed point. You can just work with the given function and fixed point, but you can also experiment with changing one or both of them.
  • An interesting Youtube video showing several different applications of average rates of change.
  • Khan Academy has an enormous number of videos on pre-calculus and calculus topics, and you should feel free to search the site for topics on which you would like some additional explanation. (If there is a drawback to Khan Academy videos, it is that they concentrate on procedures more than reasoning and conceptual understanding, but they are typically very good on the procedures.)
    A Khan Academy video on Average Rates of Change.