Looking for a calc book with nothing but problems

[bpatrick]

Main Question or Discussion Point

Ok, so I'm well beyond the level of learning calculus / analysis, so I don't need a text book with all the teaching nonsense in it, but I'd like to still develop my speed and flexibility when it comes to solving integrals ... mainly due to eventually being a TA / professor and possibly having to encounter really tricky ones and being able to do them with total ease on the fly.

So I have probably 5-6 calculus books and have worked all the problems in each of them, but the one thing that is a bit unfortunate about them is that, for example: I can turn to page ### and pick problem xx and do it, BUT since I can't turn off my ability to read, I know darn well it's in the section of the book where the problems are designed to be solved with a substitution followed by integration by parts ... which makes the problem pretty cut and dry since I can obviously do that.

Now I may be crazy and my memory deceiving me, but I swear that at some point in my early calculus career (so any of maybe 3-4 professors) had once talked about a book containing 1000+ integrals to solve that were not labeled or in sections based on how to solve them or anything like that.

This type of thing really is of interest to me and I thought I'd ask the PF community before I go emailing out of nowhere a few of my old profs asking if they were the ones who were talking about this ... OR if anybody on here knew of said book or one very similar to it that I could find on amazon/ebay for cheap.

It would be really sweet if I could solve 5 totally random integrals a day for the next year (taking weekends off) in addition to my other math learning and whatnot ... just to stay really quick and beastly with my calculus for when I'm teaching it.

Thanks for any help.

p.s. I am not thinking of "The Humongous Book of Calculus Problems" ... although that may be fine, I am just afraid that something like that is too easy, not devoted enough to integrals, and also is divided up into sections so you pretty much know how to go about solving it before you even see the problem.

p.p.s. well it may be that I was thinking of the Gradsheyn and Rytzik which makes sense because one of my early calc profs was Russian and he may have just been solving random integrals from the tables in there, but that's still not as cool, like you still know what section it's coming from and probably how to approach the solution ... and often those could be absolutely daunting, half of what I'm looking for is also a nice tool for being able to train for fast solutions of GRE style integrals that I may encounter (aka around 2-3 min to solve if you're good), in addition to just being BA at integral calculus.

 

[clanijos]

This amuses me:

I don't need a text book with all the teaching nonsense in it

Also, I would LOVE to obtain a book like the one you describe as well! Practice makes perfect, and it's hard to practice without problems...

 

[bpatrick]

Also, I would LOVE to obtain a book like the one you describe as well! Practice makes perfect, and it's hard to practice without problems...

yeah, well after loads and loads of looking online and trying to remember what prof it was, I think it might have been my one russian prof therefore he was more than likely talking about how he just opened up that huge 1000+ page table of integrals and started solving them for practice.

I know there's a Schaum's book of 3000 calculus problems, but after you figure 500 for limits, 1500 for differential calc, you may have 1000 integral problems, although I doubt they're much better than the ones I can find out of any old calc book that's in either a math library or public library, and I'd bet that they're all categorized based on how to solve them anyway.

Maybe what I had been thinking of doesn't exist but was just my misinterpretation of a description of the Gradsheyn and Rytzik. BUT if anybody has any knowledge about something like what I'm talking about, I'd love to know ... evidently so would clanijos too :-)

 

[Nebuchadnezza]

http://www.2shared.com/document/D6szXApS/Integrals_from_R_to_Z.html

http://www.matematikk.net/ressurser/matteprat/viewtopic.php?t=24242&postdays=0&postorder=asc&start=0

http://www.artofproblemsolving.com/Forum/resources.php?c=87&cid=184

http://www.mathematica.gr/forum/viewtopic.php?f=9&t=7842&start=20

This should give you enough to chew on for a while

Just tell me if you want more, I am sort of writing a calculus based book. A short intro to each section, then problems problems problems...

 

[bpatrick]

wow, All I've even looked at is that first 20 page pdf, and I'm pretty sure just that one will keep me busy for 3-4 months if I'm picking 5 a day (in addition to working on my normal "higher math" stuff).

Thank you very much, I'll be sure to check out the rest of the links too. Good luck with the book writing. Definitely let everybody at PF know when you finally get it finished, I'll surely give it a go / use it as a teaching aid.

I just had another idea too: download as many former Putnam exams as I can get and start solving those too ... just to keep sharp.

p.s. and I just downloaded the several hundred integrals from the Japan-integral forum thing ... I'm good for the next year at least, thanks very much.

 

[Nebuchadnezza]

Now what you could do, is write of all the nice interesting problems in your calculus book. Cut them into small papers and put them into a hat.

Then you would start on the problems I gave you, when done, or mostly done. Pull a few notes from the hat. If you do not have a super memory remebering where each problem came from 6 month later would be near impossible

I am also interested in seeing all of these nice integrals, as I am currently piling up integral only questions for my book.

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After you have done a lot of problems, I recomend you looking into the "Integral Bee" competitions. These are competitions where the participant need to solve 25 integrals in 20 minutes.

Now If you practice really hard, you might be able to do 20 of them. Taking these tests could be a good indication of your current skill level. As these are ment to be quick problems if you see the trick

http://web.mit.edu/abhinavk/www/integrationbee/qual2011.pdf

Just an example from the MIT Integral Bee this year, many schools have this so a quck google search will suffice

 

[paulfr]

This is a highly regarded book with tons of problems

http://www.calclifesaver.com/ [Broken]

 

[clanijos]

I have that "Calculus Lifesaver" book, and it is fantastic! Does contain a lot of "Teaching Nonsense" though, so it's probably not exactly what you are looking for.