learning calculus - where to begin?

[krez]

Hello,

 

I want something productive to do over the Christmas break and would like to learn calculus. I have a pretty good understanding of Algebra, but know nothing about calculus. I am wondering where I should begin. Are there any books or lessons you people would recommend I purchase? I learn pretty quickly, and would like to be very proficient in calculus by the time the winter break is over. What I am basically looking for is a starting point and some good study materials. Can anyone help me?

[ydoaPs]

MIT has some video lectures available.

and

[DJBruce]

I assume that when you say algebra you are including things such as limits and other pre-calculus topics. If you have a good handle on that I would start with differential calculus, Cap'n has a very nice terse introduction to differential calculus in the GUT section here. The Khan Academy also puts out a lot of very nice videos on Calculus, as well as other mathematical topics. Personally I used Calculus: Graphical, Numerical, Algebraic and Calculus of a Single Variable: Early Transcendental Functions, and liked the books. However, if I were you I would check the local library and see what books they have.

 

Finally, if you have any questions don't be afraid to ask them here.

[ydoaPs]

The lectures to which I linked are free, btw.

[the tree]

First up, good for you. It's always nice to see someone motivated and wanting to learn something beyond the structure of the education system.

 

Now the first thing that you want to learn is differential calculus, or specifically the technique of differentiation. Given that you're working in a limited time frame I think it would be a more realistic aim to get really good at that than to steam through and learn the ins and outs of integral calculus as well.

 

If you read the GUT thread that DJBruce linked to - then search around for some relevant exercise sheets then you should be well on your way.

[krez]

Thanks for all the info guys, it was exactly what I was looking for. As soon as this semester is over I am going to get started on it. Those online MIT lectures are very nice, I will save them onto my computer for later use. I dont have much knowledge of limits or pre-cal topics, but I will check out those links in the GUT section.

 

Thanks again for the info.

[hobz]

Also give Calculus Made Easy by Silvanus P. Thompson a look. It is almost 100 years old, but it has focus on the differentials, which is almost completely ignored in modern texts.