some curated calculus video, notes, and software sources
Most are likely familiar with KhanAcademy's math videos and corresponding problem sets. In my view the problem sets are good for "drill and kill" style problems and they are well mapped out. With all due respect, Khan's math videos themselves are middle-of-the-road in terms of quality. This is likely due to lack of planning.
He doesn’t use a script. In fact, he admits, “I don’t know what I’m going to say half the time.” - Washington Post, 2012
Here are several video producers that feature superior calculus content.
- https://www.youtube.com/user/patrickJMT Plain video production (hand + black marker on a whiteboard) and very tightly focused, usually starting with a short (<30 second) motivation and then a fully explained example problem. Great for seeing examples of problems being carefully solved.
- http://www.midnighttutor.com/math_tutor_online.php Special mention for not even being on youtube (well, actually). These are longer (15-30 minute) videos that go into great detail, usually dealing with multi-part problems of difficulty at or slightly above the Advanced Placement level.
- https://www.youtube.com/user/turksvids Screencast of a digital whiteboard, of particular value to AP Students are the AP Calculus Free Response playlist where several years worth of previously released exam problems are solved step by step.
- https://www.mathtv.com/ Again, not originally on youtube (although) but well worth mentioning for lots of example problems solved similarly to PatrickJMT.
- https://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/ MIT's videos are of mixed quality, and Herb Gross's 1970 series of calculus videos is a treasure. Each is ~90 minutes long, and he delves into considerable theory, but his presentation is extremely clean and well prepared. It is interesting to note that he starts each video calm and perhaps stilted, but after a few minutes he gets into a groove and you can see he is genuinely excited about the material.
There is no be-all-end-all one-stop-shop for notes and problem sets and examples, but if such a website did exist, it would be...
- Paul's Online Math Notes http://tutorial.math.lamar.edu/
It features cheat sheets for algebra and trigonomoetry, thorough notes on single-variable and multi-variable calculus, a very searchable and easy to navigate website (CTRL+F will be your friend), and every subtopic has its own page of practice problems with worked solutions hidden behind a little "show solution" link. (So you don't have to worry about leaving the page to see the solution, or seeing a solution before you're read.) No sign in necessary, no annoying cookies, just pure mathematics for your scrolling pleasure.
There are only two tware packages worth considering, in my view. Which one you prefer is up to you.
- http://www.desmos.com/calculator - Simple, easy to use, designed from the ground up by a team who listened carefully to the needs of math students and math teachers. It's snappy and responsive, allows you to save graphs as a permalink without needing a sign-in, and allows you to interact with any graph by creating "sliders" for parameters. (example: type y = mx+b and it will ask you to make a slider for m and b, type f(x) = a*sin(bx+c)+d and it will ask you to make sliders for a,b,c, and d.) You can compose functions, differentiate and integrate functions, plot inequalities, restrict domains, it's a dream. Follow @giohio on twitter for magnificent examples of what is possible.
- http://www.geogebra.org - Much more functionality Desmos because it is also a geometry package and a statistical package with a slightly more powerful computer algebra system, plus a nice forum with an active development community. Again, @giohio on twitter will post remarkable examples of geogebra doing beautiful and elegant. Not quite a snappy and responsive as Desmos, but still very good.
- Not really pieces of software, but worth mentioning are http://www.wolframalpha.com which is marvelous for checking answers to problems and http://www.symbolab.com for checking answers and seeing fully worked solutions that explain most problems in a way that mostly makes sense.