<p>I'll be taking Calc I & II this upcoming year in college and was wondering if any of you could give me advice on a few "self-study" calc books i could look into or youtube vids. I took AP Calc AB in highschool, but my teacher failed at teaching and i slacked off basically. I've never been good in calc i guess, so anything that would work for a beginner like me would greatly help. thanks.</p>

<p>You probably won't need to do anything over the summer. I was in your exact situation a year ago, took two semesters of calculus my freshman year, and did just fine. But if you're particularly concerned, most students have trouble with the algebra and trigonometry than the actual ideas of calculus. Review that, if anything.</p>

<p>Yeah I'm taking business calc right now, and the calc part is easy, but the algebra part of it is pretty tough.</p>

<p>it's as simple as going to class and keeping up with homework, nada mas. But most students don't do this and get B or below. There are some outliers. Like some people never show up to class but they ace all the tests and get an A, whereas others work hard to squeeze off B+ or A-.</p>

<p>Your algebra has to be solid. Know how to factor polynomials (especially when the coefficient of x^2 is not one), know how to factor the difference of two squares or the sum or difference of two cubes, how to "complete the square," know your properties of exponents and logarithms, how to factor partial fractions, long division of polynomials, etc. Get any kind of book meant specifically for self-study (not a textbook) and study the following topics:</p>

<p>For calc I:

-limits

-finding a derivative with the limit process

-be sure that you understand PRECISELY what the derivative is, the derivative of a function returns the slope of that function at that point, if you don't have this conceptual understanding down pat and only know how to do formulas, you are setting yourself up for failure, especially come word problem time

-derivative rules (power rule, quotient rule, product rule, log rule, etc.)

-trig derivatives (I can't stress this enough, you need to be rock-solid on trig or you will fail calculus, study trig identities in particular, study the unit circle, etc.)

-graphing functions, this means knowing about inflection points, critical numbers, concavity, etc.</p>

<p>For calc II:

-antiderivatives, indefinite integrals

-definite integrals

-sigma notation and Riemann sums

-area under a curve, be sure you understand how the definite integral is the area under the curve, some proofs are esoteric and others are more intuitive. If you don't understand the "why" then find another book or source onlines--lotsa websites and proofs online

-u-substitution

-trig substituion

-log rule, power rule, etc. for integration

-integration by parts (VERY IMPORTANT)

-area between two curves

-area of a circle, torus, etc. found via integration

-volumes of solids, pipe method and disk/washer method.</p>

<p>As far as applications go, it wouldn't hurt to be familiar with the following:</p>

<p>For calc. I:

-Newton's method

-related rates problems (these are word problems, like if a man two meters tall walks at 1.2 meters/second away from a lamp post which casts a shadow 1.5 meters long when he begins walking, at what rate is the tip of his shadow moving after eight seconds. Expect sliding ladder problems)</p>

<p>For calc II:

-Physics-related problems, Coulomb's law, Newton's law of universal gravitation, work with a constant force, work with a spring force, etc. Like how much work (work = change in energy) does it take to pump x water out of a tank with these dimensions at this rate, etc., you'll see what I mean).</p>

<p>I'm probably biased, but here is the best piece of advise you'll ever find:</p>

<p>Go to YouTube</a> - Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2006</p>

<p>It's an entire MIT calculus class of lectures, recorded for your convenience. You can also download it onto an iPod, if you prefer. MIT also provides all relevant course materials for it.</p>

<p>Need to brush up on a topic? Just watch their lecture on it, or do the problem sets assigned for that lecture.</p>

<p>Also, although it's only tangential here: Never take business calculus. It's a bastardized course that teaches the process without explaining how or why it works. It might meet your graduation requirements, or cover the math you'll need in your business courses, but it's more or less useless if you ever want to take any other courses in college.</p>

<p>The Khan Academy has the clearest lectures anywhere on the web, IMO. They really give you an intuitive understanding of the topic.</p>

<p>First go to the website of your school and find out who are some of the profs that taught the class last semester you're skipping via AP credit. Then email one of them and ask for a copy of the syllabus. That will give you an idea of what you're supposed to know.</p>

<p>The links above are good for video material, but you don't learn calculus by listening to lectures. The key is to work problems, and I have just the book for you. Get one of the books called "Calculus Problem Solver Guides" (a few publishers produce them) and then open up to a chapter covering the material you're supposed to know. Cover up the answers, work a problem. Then look at the fully worked-out solution and see if you did it right. Keep doing until you're getting the problems right, then go to the next topic. Actually this is a good idea for the class when you start in the fall, too. Practice really does make perfect.</p>

<p>"3000 solved problems in Calculus" is an ace book for practicing. </p>

<p>Another great book is "How to Ace Calculus."</p>

<p>(Both are on Amazon.)</p>

<p>advice: Dont sweat calc. Its not such a big deal. just practice all of the time and you'll get it. If not, then just take it again</p>

<p>have u taken calc in high school before?</p>

<p>edit

sorry i just saw that u did mention taking calc and having trouble, i must have skimmed it. if u remember what u struggled with, try spending the summer focusing on that aspect. i'm kind of sloppy in my algebra so i spend a lot of time on that.</p>