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Calculus I
Rhino
TheRhinLOLRegistered User regular
TheRhinLOLRegistered User regular
In college, what are the topics for Calculus I?
I'm looking for an outline or study guide to go by. I have lots of free time and want to self-study this before next semester (which will be super busy)
The course guide had this to say:
But that doesn't give me a real plan of action. I have a bunch of old calculus books and library card. Just not clear were I should start and what I need to study.
I'm looking for an outline or study guide to go by. I have lots of free time and want to self-study this before next semester (which will be super busy)
The course guide had this to say:
This course is a thorough treatment of differentiation and an introduction to integration. Topics include
the definition of derivative, limits and continuity, differentiation, applications of the derivative, definite
and indefinite integrals, the Fundamental Theorem of Calculus, techniques of integration, and
applications of integration.
But that doesn't give me a real plan of action. I have a bunch of old calculus books and library card. Just not clear were I should start and what I need to study.
Rhino on
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I would look over what a limit is, usually one of the first chapters in a Calculus book. After that comes derivatives, then finally integrals. You can check out khanacademy.org and search videos and practice exercises on Introduction to Limits, introduction to derivatives, and if you're really feeling up for it, introduction to integrals. The videos should continue on in order, and the ones I've watched seem okay.
I would definitely hit the 'practice' link at the top of the page and head down to the Limit and Derivative section at the bottom to see if you're understanding the stuff. You can even earn math achievements!
You need to know the following prerequisites: exponent rules, logarithms and exponential, function composition, difference quotients, and some basic root finding (like Quadratic Formula)
You'll study (roughly in order): Limits, Derivatives defined as limits, Power Rule, Product Rule, Quotient Rule, Chain Rule, Implicit Differentiation, Related Rates, Critical Values, Second Derivatives, Optimizations, Riemann Sums, Integral Rules, U-Substitution, and Integration by Parts.
All these topics should pretty well jump out at you.
I know a lot of people are into khan academy, but I hate that there's no degree of interaction.
Try the MIT open course-ware and find a Calc I course to watch. You still can't ask questions, but at least the students in the class will ask about the tricky parts and most of the things you'd want to know.
Overall, its nothing more than fancy algebra. You'll get further along by really shoring up your Algebra skills and the Prerequisites than by working ahead in the book.
Nintendo Network ID: PhysiMarc
0431-6094-6446-7088
My pre-calc is pretty strong. College level I've taken College Algebra (4 credits), Trig (4 credits), Re-Calculus (5 credits). I received a B in first two and A in second, with honors [as it is just basically the same algebra/trig topics, but more focused on functions).
Thanks, that is exactly what I wanted to know! I'll work on those chapters before next semester.
Would this book be ok? http://www.amazon.com/Calculus-James-Stewart/dp/0534359493
The reason I ask is because it's very cheap compared to the new editions. I don't know what book they'll use next semester, so don't want to drop tons of money.
That book is the one I'm using and it's fantastic. The introduction gives information about how calculus came about that really helped me contextualize it. I say grab it.
I used that book for Calc I - III, the same edition. You won't need a new edition for studying, you might want to buy a new edition if the class you take uses one, as the problems at the end of each section will most likely be different.
I'm current teaching my regular Calc class with Stewart's 7th Edition (which is maybe not the best choice for a basic Calc group) and AP Calculus using Hughes-Hallett, Gleason, et al. And I agree, brush up on your algebra and trigonometry. Very often complex problems involve like 10 algebra steps and 1 bit of calculus in the middle. Like an Oreo.
IOS Game Center ID: Isotope-X
If Stewart doesn't do much for you there's also a book by Ron Larsen that is considered a bit more user friendly, again any edition will do.
Prior to Stewart taking over the whole damn field the best book out there was "The Calculus" by Louis Leithold. I personally think that one is my favorite and I'd use it for my classes if the damn thing was still in print. Leithold died and the book stopped being published.
If you want things from a very technical perspective there's also Michael Spivak's "Calculus" Its not really for the faint of heart though.
I would in no way recommend Spivak. It is certainly an option for high school students who are in an Honors based program (though I've yet to find a HS student who used it), but it is not a "calculus" book. It's a real analysis book - and he says so up front. It's a good analysis book that treats the subject differently than most analysis texts, but its still likely too advanced for the OP.
They are pretty cheap on ebay 60-70 bucks or so, and because they are durable so going used will likely land you with a working one, but going from a 83 to an 89 makes the homework so much easier.
What about a Ti-84 Plus? That is what my [college] algebra teacher suggested, she said it would be good up to undergrad Calc 3
lol, wut:
http://i.imgur.com/ZH4Yl.png
Yep, I have one and it's served me just fine! (Disclaimer: I did change majors before Calc 3.) That was the recommended calculator for me; one of my classes actually REQUIRED a TI-83/84 graphing calculator for some reason, and I happened to find it on sale. I don't have any experience with the TI-89, but I got the feeling it's supposed to be a "fancier" calculator than the 84 Plus. More features, etc. I could be wrong. But I like how the 84 does things, for the most part, so it should be a perfectly acceptable calculator.
An A is an A and if the calculator is legal to use in class then use it. I'm not suggesting loading test notes on the calculator (which you can do but it's cheating) I'm suggesting using a tool available and usually encouraged to solve equations faster and easier.
Some teachers might not let you use an 89 because they are so powerful and can do so much. The 83 or 84 is guaranteed to be okay. So I'd recommend against the 89.
And if I can get on my high horse for a moment, if you need an 89 to do the math for basic calculus classes, then you don't know the math. If you need that kind of functionality to solve the problems you'll be asked, MatLab will be made available and the test will be in the computer lab, if you don't need it, I think it's kind of cheating to have it available on your calculator. Learn the math and don't rely on a crutch like an 89. Many of my calculus tests didn't allow calculators of any kind anyways - they didn't use specific numbers and expected you to solve general forms, not even an 83/84 necessary. If you've been doing all your homework with an 89 up until then and have gotten used to relying on it, you'll be screwed on exam day.
^pretty much this.
I've been using a TI-86 since 1997. Its gotten me through High School, Undegraduate, Economics Graduate School, Math Graduate School, and I use it virtually everyday while teaching college math. They're usually about 25 to 35 dollars on Ebay.
Except that the people who didn't use the 89 now know how to actually do the math they were tested on. One of the most important things I've learned in life is that experience trumps everything. Someone who has worked out those problems by hand has the advantage of experience and at some point, maybe often, maybe just once depending on what field you go into but at some point, the person lacking that experience will be completely stumped by a problem whose solution is obvious to the person with that experience.
I'll give you an example that's accessible to everyone. Fractions. Almost no students learn to work with fractions anymore. Why? They have a calculator, why bother? But then I see a student spend five or ten minutes working on a problem, multiplying numbers with three or four decimal places, often giving up or even arriving at a wrong answer when the problem would have taken three whole seconds to resolve if they'd used fractions rather than decimals.
And this is overshadowed by the fact that the people who never put in the effort to learn to work with fractions cannot advance through algebra. No calculator will turn even the relatively simple (a/b) into a decimal. If a student doesn't do the work he will hit a brick wall.
Unless your chosen career requires a degree with ridiculously unnecessary levels of math you're setting yourself up for a similar problem if you rely on the calculator. It is important to ask yourself whether you are trying to get a grade or trying to learn; the two are not equivalent.
0431-6094-6446-7088
The example of fractions are so fundamental that everyone has to use those. Which is why teachers demand you to show your work, however on those there are programs that will simplify fractions for you in letter format so even there you can skate by. In fact I do believe the TI-89 can simplify expressions.
Thanks guys for the suggestions. I'll say we can close this thread as I don't want it to turn into a holy war about calculator models
I'm going to stick with the Ti-84 Plus for now. That is what my teacher uses and what is suggested for class.
It can also explain (sorta) steps to a problem if you're not following or just want to check those even numbered homework problems.