Useful Links
I will add links to other websites 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.
- Wolfram Alpha is an online symbolic calculator. You can use it, in particular, to find anti-derivatives of many functions.
Useful (or just Fun and Interesting) Videos
- Here are the Apollo 15 Hammer and Feather Drop video that we watched in class, and the Peep Show Moon Landing comedy sketch. (British comedy, so listen carefully for the jokes!)
- Here is The Theorem of the Mean Policeman video that I mentioned in class. (Thanks to Jeremy Wissell for finding this link.) I haven’t watched all of them yet, but there are links to a lot of other interesting-looking videos on the same page.
- Here is the Can Dogs Do Calculus? video. (If you are interested in reading it, here is the original paper the students refer to at the start of the video.)
Definition of the Integral (Riemann Sums)
- A Desmos page in which you can approximate areas under graphs with “Riemann sums”; i.e. by approximating the area with the sum of the areas of rectangles.
Numerical Integration Methods
- A Desmos page in which you can evaluate integrals numerically using various numerical methods, including Simpson’s Rule.
Integration Techniques
- Two nice summaries of the method of rewriting a rational function in terms of its partial fractions, from PurpleMath, and from Paul Dawkins at Lamar University. (The latter has a very nice summary of the forms of the partial fractions which occur in the various cases, and is also set up so that you can solve each example yourself before reading the solution.)
- If you prefer to watch videos, here is one from Khan Academy.
Differential Equations
- Googling “Desmos slope fields” brings up many links. Here is one nice example. (Replace the function g(x,y) by the appropriate function for the first-order equation that you want to analyze.)
- This version allows you more flexibility to change the region in which the slope field is plotted.
Mathematical Modeling
- Mathematical Modeling is one of the “conceptual categories” in the Wisconsin/Common Core high school mathematics standards. This web page refers to a diagram of the modeling cycle, which appears to be missing. You can find it on this page. (There are lots of interesting posts on that mathematical modeling blog.)
Kevin Mcleod
08/31/2019