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Sayonara

Calculus 101?

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Despite a lengthy and intensive period in the education system, I am one of many thousands of people who was never introduced to Mr Calculus.

 

If someone could make a "Calculus for Dummies" style thread, it would be most appreciated. I'd be very interested in learning about the method and application of this theory.

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My two favorite calculus things:

 

The integral of ln(x) is x*ln(x) - x

 

 

integral of uv is uv - intg(v*du)

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Originally posted by Sayonara³

"Calculus for Dummies"

Hint hint.

 

:)

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Very roughly, Calculus is a branch of mathematics that deals with the measure of change.

 

Here are some links to get you started:

http://mathforum.org/library/drmath/view/51436.html

 

I'm assuming you're perfectly caught up on your precalculus concepts...

 

Learning from the web is the worst way to learn calculus. Buy a good textbook.

 

I heard Anton is great:

 

http://www.amazon.com/exec/obidos/tg/stores/detail/-/books/0471153060/contents/ref=pm_dp_ln_b_2/104-7890783-6061567

 

Some people in #math (on efnet) said they have used Stewart

 

http://www.amazon.com/exec/obidos/ASIN/0534362982/qid=1027212824/sr=1-1/ref=sr_1_1/104-7890783-6061567

 

This book from Spivak is an excellent calculus book and can help you prepare for Analysis (a more generalized term for the branches of math that involve calculus)

 

http://www.amazon.com/exec/obidos/ASIN/0914098896/qid=1027213056/sr=2-2/ref=sr_2_2/104-7890783-6061567

 

 

I'm planning on buying Spivak soon to see how it is. I can make a review of the book later on if you want.

 

 

I'd give an intro, but I'm terrible when it comes to teaching :) (besides I'm still learning this myself!)

 

Anyway, good luck!

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Thanks for the references Epsilon.

 

I'll have a look at those tomorrow when I am less drunk/tired.

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bob millers calc for the clueless

alone the book might not do too much since theres a lack of examples and questions, it's meant as an add on. it's very good and in english, bob miller is supposed to be the best professor in the world for calculus, funny thing is that im taking calc 2 this summer and having a hard time with it, calc 1 wasnt bad but calc 2 is much harder for me and the shortened semester is making it too fast, but bob miller is supposed to be teaching at the college im taking the class at ,City College of New York (CCNY), wouldnt it have been REALLY nice if HE could have been my prof. :rolleyes:

that book is good though, if i had taken calc 2 in a normal semester and known about the book form day one.. it would hae been MUCH easier.

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I would suggest getting brushed up on the pre-calc topics well before you start looking at the calc. Especially trig. Much of my first calc course was working with limits and d/x using trig. It is easy to learn the basics of single variable calc, it adds a whole new step when you throw in the challenge of trig and the unit circle.

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Originally posted by fafalone

 

 

integral of uv is uv - intg(v*du)

 

er is it?

 

you sure?

 

isn't it

 

int(u * dv/dx) = uv - int(v * du/dx)

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Let's look at an example...

 

 

intg(ln x)

 

u = ln x

v = x

 

uv - intg(v du)

 

= lnx*x - intg(x*1/x)

 

= xlnx - intg(1)

 

=xlnx-x

 

 

take the derivative to prove it:

 

d/dx xlnx-x

= lnx+1 - 1

=lnx

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Originally posted by fafalone

Let's look at an example...

 

 

intg(ln x)

 

u = ln x

v = x

 

uv - intg(v du)

 

= lnx*x - intg(x*1/x)

 

= xlnx - intg(1)

 

=xlnx-x

 

 

take the derivative to prove it:

 

d/dx xlnx-x

= lnx+1 - 1

=lnx

 

er

 

if you're doing int(ln x) then u=ln x and dv/dx =1, therefore v does = x

 

i think we're saying the same thing..almost

 

originally you said you were doing the integral of uv which would have been the integral of xlnx but you're not.

you're doing the integral of u * dv/dx which is what i said

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yes

 

so:

 

"integral of uv is uv - intg(v*du)"

 

is not right

 

it's:

 

int(u*dv) = uv - int(v*du)

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You don't "touch Mr. Calculus." You command him to vanquish you enemies and hope like hell that he doesn't turn on you.

 

 

Best thing to know: "The definite integral is a sum of an infinite number of algebraic products, one with a factor of which, in the limit, becomes infinitely small."

 

This is for things you can graph, likes area and arc lenghts. But in the abstract, the known and potential applications of calculus are immense.

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Originally posted by Sayonara³

Despite a lengthy and intensive period in the education system, I am one of many thousands of people who was never introduced to Mr Calculus.

 

If someone could make a "Calculus for Dummies" style thread, it would be most appreciated. I'd be very interested in learning about the method and application of this theory.

 

I'm reading the book called Calculus Demystified. It's similar to a Calculus for dummies. It has little exams and stuff in it to see if you comprehend.

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Whatever you do, DONT TAKE PRECALC! Save yourself... I allowed myself to get sucked into the trap, and now I am stuck in a room where time is infinatly slow... Just take calc. Right now in pre-calc I'm just doing calculus and the teacher isnt too happy, but who cares...:mad:

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Originally posted by Ragnarak

yes

 

so:

 

"integral of uv is uv - intg(v*du)"

 

is not right

 

it's:

 

int(u*dv) = uv - int(v*du)

 

rag's correct.

 

in the case of intg(lnx), if you make lnx = u, then your dv=1. your dv needs to be present, not your v.

 

~Wolf

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When finding the derivative of something; there's little shortcuts...ie. power of a funx rule, product rule, etc. etc.

 

Are there any shortcuts for the integration of a funx?

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