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Integration-By-Parts Man!

FortKnox (169099) writes | more than 10 years ago

User Journal 21

Heh, my old roommate used to refer to me as "Integration-by-parts man" because I was really good at integration by parts. Last time I used integration by parts was calc III (maybe calc II). I don't think I ever needed complex enough integration in any of my core classes to require integration by parts.Heh, my old roommate used to refer to me as "Integration-by-parts man" because I was really good at integration by parts. Last time I used integration by parts was calc III (maybe calc II). I don't think I ever needed complex enough integration in any of my core classes to require integration by parts.

One of my family friends is in college (my school, my degree with some influence by me) who is having trouble with it. Seeing that I took calc3 in the beginning of 1996, I'm a little nervous about teaching (let alone seeing if I remember it well enough to work the problems myself). I don't have my calc book anymore, so it looks like I'll have to peruse the web to a page that has a little explanation to jog the 'ol noggin and maybe some problems I can work through. I don't suppose anyone knows a site like that (I really do not want to pay $100 for a calc book, if at all necessary).

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It came back to me surprisingly well (1)

johndiii (229824) | more than 10 years ago | (#8260763)

My daughter has calculus (BC, if that means anything to you) this year, and I've been helping her with it. Despite the fact that they have a terrible text, I was able to recall quite a bit of the calculus that I had last studied in 1983 (diffEQs; other calc even older). Once I got started, it all flowed really well. Your mileage may vary, of course.

Last time I did it... (1)

Some Woman (250267) | more than 10 years ago | (#8260782)

Ummm...yesterday? After a two year hiatus, ole IBP is back! And crazier than ever! Gone Wild, I tell you!

And No. I don't know of any resources. Might try going to Barnes and Noble- they might have a tutorial that you can peruse in the store.

Re:Last time I did it... (1)

FortKnox (169099) | more than 10 years ago | (#8260836)

I may do the barnes&noble thing (well, i'll do the 'borders' thing, since its closest).

Re:Last time I did it... (2, Funny)

robi2106 (464558) | more than 10 years ago | (#8262324)

Calculus Gone Wild!

You've never seen Calculus like this before!

Un cut and uncensored!

Buy now and we will throw in, absolutely free...

Calculus Spring Break!

jason

I actually used it once... (1)

dmorin (25609) | more than 10 years ago | (#8260815)

Oh lord, let's see.....the integral of u dv is equal to uv times the integral of vdu? Something like that.

I got to use it once, about a year out of college, when I worked for a digital signal processing group and we wanted to check something manually to see if it was approx. the expected result.

just remember ... (1)

Abm0raz (668337) | more than 10 years ago | (#8260880)

V(du) = UV - U(dv)

-Ab

Re:just remember ... (1)

FortKnox (169099) | more than 10 years ago | (#8261125)

yeah, I've looked back into it. Hope it would rush into my mind, but I had to work out a couple problems to get my mind refocused. I think I got the hang of it again... :-)

Book price (1)

Tet (2721) | more than 10 years ago | (#8261527)

I really do not want to pay $100 for a calc book, if at all necessary

So don't. I know that text books are expensive in the US, but they don't have to be that expensive. Anyway, the book you're looking for is "Engineering Mathematics" (or possibly "Advanced Engineering Mathematics", check the contents of both), by K.A. Stroud. Amazon US have it for US$60. It's cheaper from Amazon UK, although check the shipping price (I can ship it for you if necessary).

I think I speak (1)

blinder (153117) | more than 10 years ago | (#8261592)

for all (or most... err, or just some) of the humanities (and the like) majors out there when I say:

Huuuuhhhh?????

Re:I think I speak (1)

robi2106 (464558) | more than 10 years ago | (#8262251)

Yay for derivitives!

Calc III unlike the previous two classes, was kind of fun. I mean... You get to deal with vectors, and fun visual stuff and math in 3D.

jason

Re:I think I speak (1)

mekkab (133181) | more than 10 years ago | (#8262635)

And when you went on to take "Fields, Matter, and Waves I" and "Fields, Matter, and Waves II" you got to see your calc 3 actually do useful stuff (once you got beyond the effect of a point charge in a vacuum on a gaussian sphere of radius 2m and all that other drivel), like see how curls actually had some meaning in the physical world (the right hand rule).

Hooray for the cross product! Hooray for the Del operator! Hooray for Maxwell!

Re:I think I speak (1)

robi2106 (464558) | more than 10 years ago | (#8270531)

Yeah.... too bad I didn't get in to any of that (or may be it is good...who knows). I was in a Chemistry major program so that is why I took CalcIII. The next class would have been Physical Chemistry, which I hear was so much more math than chemistry.

But I switched to computers to avoid the evil Organic chemistry class. Well that and I kept getting summer jobs in computers instead of chemistry so I eventually took the hint.

jason

Re:I think I speak (1)

mekkab (133181) | more than 10 years ago | (#8262699)

Just keep nodding and welcoming your Calculating overlords (read: Macintosh).

Calculus is the mathematics of change. Just remember that you too, are a vector. Now get your vector ass back to work or I'll integrate you by parts! ;)

Re:I think I speak (1)

blinder (153117) | more than 10 years ago | (#8269175)

Just keep nodding and welcoming your Calculating overlords

its what i *do*! :-D

Now get your vector ass back to work or I'll integrate you by parts! ;)

damn you mekkaman!!!

in Mekka's Russia parts integrate you!

Beautiful Integrals (1)

Morosoph (693565) | more than 10 years ago | (#8262925)

How about this one: Integral {e^-(x^2)}dx between -inf and -inf?

How to find it is sheer beauty...

Let I=Integral {e^-(x^2)}dx, then I^2=[Integral {e^-(x^2)}dx]*[Integral {e^-(y^2)}dy]

Since x and y are independent variables, I^2=Integral Integral {{[e^-(x^2)]*[e^-(y^2)]}}dxdy

so I^2=Integral Integral {{e^-[(x^2)+(y^2)]}}dxdy

I hope that my fellow mathematicians will allow me to skate over the rigour here (as I'm a little^H^H^H^H^H^H^H^Hvery rusty) whilst I invoke geometrical intuition with a flourish of hand-waving:...

We're integrating over the plane to get I^2, so let us see what happens when we switch variables to r and t (for theta). As we sweep around the radius of a concentric circle, we find that the distance swept around is rdt in angle dt, so that (unrigourous bit) we can replace dxdy with rdrdt as a result of changing variables. Notice also that x^2+y^2=r^2 (Pythagoras), so that our integral becomes:

I^2=Integral Integral {{r*e^-(r^2)}}drdt=[Integral {1}dt]*[Integral {r*e^-(r^2)}dr]

so I^2=2Pi*Integral {r*e^-(r^2)}dr (evaluated between r=0 and r=+inf)

But d(e^-(r^2))/dr=-2re^-(r^2), so that our integral becomes:

I^2=-Pi*[e^-(r^2)] (between r=0 and r=+inf)

so I^2=-Pi((e^-inf) - (e^0))=-Pi(0-1)=Pi

ie. Our original integral I=Integral {e^-(x^2)}dx evaluates to sqrt(Pi). Beautiful!

Calculus? I did that at A-levels (Sixth Form) (1)

MonTemplar (174120) | more than 10 years ago | (#8263099)

And that was the last time I've looked at it. All of nearly... 18 years ago. :)

Ditto for Statistic. Know the principles, buggered if I can remember how to apply it.

But Logic? Yeah, I know Logic? Every which way. God help me! :D

-MT.

pulls out old 220 notes, digs through and finds (2, Informative)

http (589131) | more than 10 years ago | (#8264612)

http://www-math.mit.edu/~djk/index.html
in particular...
http://www-math.mit.edu/~djk/18_01/chapter24/conte nts.html
pain beginning behind left eye...

google is your friend (1)

TechnoLust (528463) | more than 10 years ago | (#8266082)

Search [google.com]

Integration by Pants (1)

andfarm (534655) | more than 10 years ago | (#8266492)

Heh. Funny you should mention that -- I'm learning that exact stuff right now myself. (AP BC Calculus.) My teacher has a tendency to write rather quickly, so "Parts" ends up looking rather like "Pants" much of the time. I was rather confused the first time I saw the words "Integration by Pants" up on the board, and it's gotten to be a bit of a running joke.

Check out ebay and half.com for used books.... (1)

(H)elix1 (231155) | more than 10 years ago | (#8266730)

You can find some older calc books. I took a calc refresher a few years back because I was doing some heavy number pushing again (bioinformatics) and was surprised to see the text something you would find at a $30 b&n rather than a typical $100 collage textbook.

Just for the record, power series still suck...

Psst...free book (1)

Pinball Wizard (161942) | more than 10 years ago | (#8337396)

I have an old calculus book I could send you(actually I have two, which is why I don't mind giving one away).

Email me an addy and I'll get it out to you.
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