Resources for Understanding and learning Calculus

[aeliclan]

Hey Everyone,

I am extremely glad to have found and joined the physicsforums community, and look forward to working and learning from others who share my enthusiasm. I'm currently enrolled in Precalculus, but find the class to be a little slow and really scripted towards teaching students the HOW TO, but not the Why. I am really interested in moving beyond the superficial classroom and learning Calculus on my own. I have stumbled upon a few great resources including:

Khan Academy
PatrickJmt


I plan on taking Calculus (I or II depending on how far I get in selfstudy) this coming spring at my local community college. For someone self-studying Calculus, do you think that these resources would be sufficient enough in preparing for/substituting a college level class in Cal I, possibly Calc II?

I know I'll need to practice problems, so any workbooks that you would recommend would be helpful.

In addition to the resources mentioned above, I've really been searching for a good book (or other resource) that would really walk me through the concepts of calculus and really teach me WHY and not just how. I first looked at books like "How to ace Calculus: a streetwise guide", but have read that these types of books are meant to go along with a course, and are not meant as selfstudy guides. Plus, they don't really explain the Why. Spivak and Apostol seem to be very prominent amongst the community, but after much research, I believe these books would be better approached after mastering the basic concepts of calc. I'm looking for a book that really explains the fundamentals, and everything else covered in a college course, without the rigor of an analysis book. Any help is much appreciated.

Please be as specific as you can, Thank you!

 

[micromass]

I think a book you'll like is "practical analysis in one variable" by Estep. I know it has analysis in its title, but don't let that scare you. The book is really suitable to tell you the why and the how of things. And it's not as sophisticated as Spivak. Try it out!

 

[Davidthefat]

I would say check out MIT's OCW, it can be found on Youtube, their website and iTunesU. On iTunesU, you can find other schools. Stanford and Berkeley seem to have good calculus series.

Also check out Calculus Made Easy by Silvanus Thomson. It is a classic book.

 

[micromass]

I disagree strongly with calculus made easy. It's a book that essentialy dumbs down calculus to plug and chug exercises. It doesn't provide any motivation, proofs or logical reasoning.

Judge for yourself. The book is available freely at http://www.gutenberg.org/ebooks/33283

 

[aeliclan]

Thank you Micromass for your thoughtful suggestion! I'll be sure to check it out!
In the mean time, I saw a book called Calculus: An Intuitive and Physical Approach by Morris Kline. Have you heard of this book? Reviews say that it explains calculus in a very intuitive approach and is good for self-study. Do you think this will be a good book in comparison to "practical analysis in one variable" by Estep?
Also, Is "Practical analysis in one variable" suited for self-study by a first time calculus learner?

Thank you again!