<p>What is required to learn this material? BC Calculus level math? How difficult is it to self-teach this kind of stuff? I'm aware that it's difficult, but I was thinking of looking into it, as I love math more than any other subject, and the concepts are vital for other areas like physics. Any input from someone who is taking or has taken the course would be appreciated.</p>
<p>BC calculus level math is sufficient. Multivariable calculus is just single variable calculus in multiple dimensions. It builds on the same concepts. It's no more difficult to teach yourself this material than any other higher-level math. The courses I took in it were somewhat dull, so if you have the option of learning linear algebra or differential equations instead (which sometimes have multivariable prereqs :-(. my courses did), I would do that, if you haven't already. Taking multivariable calculus after a whole year of single variable got really old for me.</p>
<p>Thanks for the reply. And what do you think would be a reasonable amount of time for me to master it, assuming I have free time and am willing to do it?</p>
<p>Introductory Calculus in college normally covers three courses which are roughly:
1. Differentiation
2. Integration
3. Multivariate Calculus
They probably also throw in infinite series.</p>
<p>If you are a math major, then you continue with courses like:
Linear Algebra
Complex Variables
Vector Analysis
Statistics
Advanced Analysis (Calculus from a theory viewpoint)
Abstract Algebra</p>
<p>As s'vrone said, Multivariate calc is pretty much expressions in multiple variable where you differentiate/integrate against only one of them. In multivariate, differentiation is easier than integrating.</p>
<p>You can consider a multivariate calc class to be equivalent to either the differentiation class or the integration class. It is hard to answer your question about difficulty since you can cover it at different levels, especially when you consider applications. You might look at:
<a href="http://en.wikipedia.org/wiki/Multivariate_calculus%5B/url%5D">http://en.wikipedia.org/wiki/Multivariate_calculus</a></p>
<p>That would be Calculus 3, which follows Calc 1 (single var differential calculus) and 2 (single var integral calculus + sequences and series). Essentially, the level of difficulty is not much different than single variable integral calculus, it's just an extension into many variables as stated by s'vrone (you cover both partial differentiation and multiple integrals in one semester). But I will disagree on the higher level math difficulty, Calc 3, once you have calc 2, is much easier to learn by yourself than actual math courses (baby algebra and analysis).</p>
<p>Any suggestions for a text that might be best for me to study with?</p>
<p>Multivariate calc is taught as part of the sequence Calculus 1, 2, and 3. Because of this, publishers either have one great big book that covers all three courses, or two books where the first book covers Calc 1 & 2, and the second book covers Calc 3. I would recommend that you check amazon to see if the textbook that you used in AP Calc BC has a follow on.</p>
<p>If you like math, you might look at a book "Calculus Made Easy" by Thompson and Gardner that was first published in 1910 with subsequent editions in 1914 and 1946. It was published again in 1998. It is obviously a classic and sums everything up very clearly. (no multivariate, though)</p>
<p>our multivariable class is using a textbook by James Stewart.</p>
<p>yeh we use that too. the brown book so-called.</p>
<p>Thanks a lot. I don't think I'll be doing this for another few months, so I'll probably be back again with more questions. I'll check out that book by Stewart.</p>
<p>Thanks again.</p>
<p>Stewart is a real busy guy. He has a sequence with a blue cover too. If you use him, they might be using the text at your college later.</p>
<p>[url=<a href="http://www.amazon.com/gp/product/053439339X/qid=1138247127/sr=2-1/ref=pd_bbs_b_2_1/104-6288864-5647959?s=books&v=glance&n=283155%5DThis%5B/url">http://www.amazon.com/gp/product/053439339X/qid=1138247127/sr=2-1/ref=pd_bbs_b_2_1/104-6288864-5647959?s=books&v=glance&n=283155]This[/url</a>] wouldn't happen to be the book, would it? The "brown book," that is.</p>
<p>I assume [url=<a href="http://www.amazon.com/gp/product/0534377181/qid=1138247559/sr=1-2/ref=sr_1_2/104-6288864-5647959?s=books&v=glance&n=283155%5Dthis%5B/url">http://www.amazon.com/gp/product/0534377181/qid=1138247559/sr=1-2/ref=sr_1_2/104-6288864-5647959?s=books&v=glance&n=283155]this[/url</a>] is the blue one...cool cover, actually.</p>
<p>Either way, they'll put a hole in my pocket at $150 apiece. :(</p>
<p>My class uses Thomas' Calculus, 9th Edition Alternate.</p>
<p>if stewart gives hard book tests, i'd punch him in the face</p>
<p>no we use this
Stewart, James. Multivariable Calculus, 4th Ed.<br>
obviously can't find the copy on the internet. really old i guess lol</p>
<p>Stewart really does have separate textbook sequences. It isn't just the edition numbers.</p>
<p>terra: The multivariable book for what you had is:
<a href="http://www.amazon.com/gp/product/0534393578/sr=1-6/qid=1138247790/ref=pd_bbs_6/002-8357183-9736048?%5Fencoding=UTF8%5B/url%5D">http://www.amazon.com/gp/product/0534393578/sr=1-6/qid=1138247790/ref=pd_bbs_6/002-8357183-9736048?%5Fencoding=UTF8</a></p>
<p>Probably a better sequence that is also more recently published is:
<a href="http://www.amazon.com/gp/product/0534437362/ref=pd_sbs_b_3/002-8357183-9736048?%5Fencoding=UTF8&v=glance&n=283155%5B/url%5D">http://www.amazon.com/gp/product/0534437362/ref=pd_sbs_b_3/002-8357183-9736048?%5Fencoding=UTF8&v=glance&n=283155</a>
and
<a href="http://www.amazon.com/gp/product/0534378633/qid=1138248504/sr=2-1/ref=pd_bbs_b_2_1/002-8357183-9736048?s=books&v=glance&n=283155%5B/url%5D">http://www.amazon.com/gp/product/0534378633/qid=1138248504/sr=2-1/ref=pd_bbs_b_2_1/002-8357183-9736048?s=books&v=glance&n=283155</a>
It is a little confusing because the first book is in its third edition while the multivariable book is only in its second edition. If you are studying on your own, you might want to also get the solutions manual for the answers to homework probs. Obviously you have to be careful that the sequences and the editions match. If you live near a college, any college, you might be able to get it at their bookstore instead of amazon.</p>
<p>Just a side note, but if you are looking for cheap textbooks, try half.com. I havent checked how much these books you are mentioning are going for, but I was able to buy some textbooks to prep for AP tests in courses that I self-studied in for 3-5 bucks apiece. Its worth a look.</p>
<p>Order it from Amazon, but dont get the most recent edition. $70 books can be bought for around $5.</p>
<p>"In multivariate, differentiation is easier than integrating." I took multivariate calculus last semester. The hardest problems involved finding the center of mass and integrating by converting between different coordinate systems. Oh yeah, I used the kewl "5th" edition steward book.</p>
<p>implicit differentiation is a thousand times easier in multivariable calculus. wow.</p>
<p>You can also order them used off Amazon. Some people sell the books pretty cheap and I know for the Stewart text that we are using for Calc, it comes in a soft-cover edition (paperback). It was a lot cheaper to buy the soft-cover one and lighter to carry around, so you might want to check that if you don't want to spend 150!</p>