Calculus
Here I hope to provide a bunch of information that I’ve gathered over the time taking Calculus as a distance learning course. Currently I’m taking courses with UIUC. As of this writing I’m in Math 231. It’s Calc II, so currently it’s a lot of splines, and Taylor series at this point. It’s difficult and challenging, but I’m coming to understand it a bit more everyday.
Some things that I’ve found useful:
Wyzant. Home tutoring service. I meet once a week with a tutor from here, skilled and very good at explaining what is going on. It’s not cheap, but it’s definitely worth it as my understanding has increased dramatically since we’ve started meeting.
Aleks. This was used in the PreCalculus course. I liked this a good deal. The basic idea is there are sections of a pie that correspond to topics to learn and then be quizzed on. This worked out for me as I could revisit topics and do the entire system at my own speed.
Thinkwell. This is a site that is like a visual textbook and distance learning tool. This has a tremendous amount of content and a full course load of videos for Calc I & II, and probably some of III. I know I’ve seen vectors in there. The teacher has a good teaching style, makes it entertaining and thoroughly covers the topics with examples. I’ve also seen this teacher in several other educational offerings, like the teaching company. It also has quizzes and tests. It is a full offering for the money.
Teaching Company. I have this set of DVD’s from this company. They’re good, but they are definitely college lectures. The professor is good at explaining the content and it’s applications, but it’s a little dry. You have to really pay attention and stay focused.
I think the professor from the Teaching Company courses actually wrote a book with the professor from the Thinkwell courses. I believe it’s called The Heart of Mathematics. Have not read it, but am definitely putting it on the list.
I’ve read:
Calculus Made Easy This was by far my favorite book. It’s very straight forward and from what I’ve read it’s a classic guide. I can see why, it’s an easy read and covers a good deal of the subject.
Calculus This is by far the most thorough and understandable Calculus textbook that I own.
Calculus II This was a good discussion about Integral Calculus, Series, and some Differential equations, but has a good deal of errors in the examples. However, it does cover this in a very straight forward voice.
A Tour through the Calculus This is a very heady thorough tour of The Calculus. You’ll need a dictionary to get through this book. If you don’t have a good grasp of the topics involved it would be tough to consume this book. I think this is probably best left to someone late in Calc II or Calc III.
On occasion, I join this chat room to ask questions or discuss Mathematics in general.
I’ve found two places that also seem to try and gather communities around courses, classhive and the latest one that I’ve found is koofers
Also a good strategy is to just try searching for the topic you’re working on at youtube. There are plenty of good tutorials and discussions on there. iTunes also has a number of Calculus courses from the likes of Stanford and MIT.
I hope this helps, good luck in your learning. If you have any other suggestions please do leave them in the comments here.