Making like Newton and learning calculus...
December 17, 2009 6:59 AM Subscribe
I want to re-teach myself calculus. Or at least its elementary principles. More detail inside.
I'm looking for recommendations for an introductory calculus textbook with which to re-learn basic calculus.
What I'm looking for:
--A text book, not "calculus for dummies." Assume at the AP/international baccalaureate/freshman college level.
What I'm not looking for:
--A text book directed toward aspiring physicists/engineers/mathematicians.
Also, the intent here is to learn on my own at my own pace, not to take a formal class. I've been out of college for over a decade, and have always found learning/studying on my own to be more effective than sitting in a class. I took calculus in high school and don't remember much of it. The only math I took in college was several symbolic logic classes as I placed out of math requirements in college.
The overarching goal here: I work in finance, though not in a quantitative/financial engineering position. However I am occasionally exposed to colleagues who work in these areas or who have a much heavier quantitative background than I, and I would like to have at least some grounding in higher level math than I presently do. I do not expect this endeavor to turn me into a "quant jock" or a financial engineer or a physicist. Etc.
Thanks.
I'm looking for recommendations for an introductory calculus textbook with which to re-learn basic calculus.
What I'm looking for:
--A text book, not "calculus for dummies." Assume at the AP/international baccalaureate/freshman college level.
What I'm not looking for:
--A text book directed toward aspiring physicists/engineers/mathematicians.
Also, the intent here is to learn on my own at my own pace, not to take a formal class. I've been out of college for over a decade, and have always found learning/studying on my own to be more effective than sitting in a class. I took calculus in high school and don't remember much of it. The only math I took in college was several symbolic logic classes as I placed out of math requirements in college.
The overarching goal here: I work in finance, though not in a quantitative/financial engineering position. However I am occasionally exposed to colleagues who work in these areas or who have a much heavier quantitative background than I, and I would like to have at least some grounding in higher level math than I presently do. I do not expect this endeavor to turn me into a "quant jock" or a financial engineer or a physicist. Etc.
Thanks.
When I took AP Calculus, the text was Hughes-Hallett. It's pretty decent. It's been, uh, a while since AP Calc, but I recall it not having much of a physics/engineering/quant/professional mathematics agenda. (You'll have a hard time finding a calc text with no agenda along those lines, since that's the primary audience of most calc classes.)
Personally, I preferred the presentation in Stewart, though it's a heck of a tome. The local math department joke is that it must have been printed on neutron star material.
I have heard good things from students about, but have not personally used, Ostebee and Zorn (full disclosure: I went to school with their kids).
posted by dorque at 7:29 AM on December 17, 2009
Personally, I preferred the presentation in Stewart, though it's a heck of a tome. The local math department joke is that it must have been printed on neutron star material.
I have heard good things from students about, but have not personally used, Ostebee and Zorn (full disclosure: I went to school with their kids).
posted by dorque at 7:29 AM on December 17, 2009
I did this about 15 years after taking calculus in college, but I already had a book. I used the book I should have been studying then. I don't remember the author[s], but it was Calculus and Analytic Geometry, about 2" thick, and was a standard-type college textbook with answers to the odd-numbered problems in the back. I would guess you could find something like this in a local library book sale.
I just went through it like I was supposed to in college (I was too busy playing chess at the time) and I felt it made sense and 'stuck'. Disclaimer- I didn't finish it, but I got about halfway through.
posted by MtDewd at 7:30 AM on December 17, 2009
I just went through it like I was supposed to in college (I was too busy playing chess at the time) and I felt it made sense and 'stuck'. Disclaimer- I didn't finish it, but I got about halfway through.
posted by MtDewd at 7:30 AM on December 17, 2009
This guy explains things slowly and clearly and goes from the ground up. His videos could take someone all the way from basic arithmetic to Laplace transforms, differential equations, and linear algebra (well beyond high school calculus, in other words). I've not tried following a whole course with him, but I think he's worth a try for your purposes.
posted by col_pogo at 7:33 AM on December 17, 2009 [4 favorites]
posted by col_pogo at 7:33 AM on December 17, 2009 [4 favorites]
Here is a list of the most enlightening calculus books. I cant really offer an opinion though.
posted by Busmick at 7:34 AM on December 17, 2009
posted by Busmick at 7:34 AM on December 17, 2009
I've heard good things about Thompson's Calculus Made Easy, but I didn't learn calculus from it personally.
posted by crocomancer at 7:34 AM on December 17, 2009 [1 favorite]
posted by crocomancer at 7:34 AM on December 17, 2009 [1 favorite]
I remember liking James Stewart Calculus a lot, and I have it around here somewhere, but man, the amazon reviews are bad, so maybe my memory is not that good? Stewart is the one basically everybody uses, with the violins and shit on the covers.
posted by jeb at 7:39 AM on December 17, 2009
posted by jeb at 7:39 AM on December 17, 2009
I just looked at Busmick's link and saw this:
"Calculus by Michael Spivak (Updated in July 2008!): I can’t praise this book high enough, to me this is THE calculus book. I"
I forgot about this book. People love this book. I never had it though. That's probably what you want.
posted by jeb at 7:45 AM on December 17, 2009
"Calculus by Michael Spivak (Updated in July 2008!): I can’t praise this book high enough, to me this is THE calculus book. I"
I forgot about this book. People love this book. I never had it though. That's probably what you want.
posted by jeb at 7:45 AM on December 17, 2009
Favoriting and seconding Silvanus P Thompson's "Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning Which Are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus". It's the book that taught me calculus when I self-studied it as a precocious 16-year-old; I later found out that Feynman studied this book as well. It covers the very basics of calculus, disposing with a lot of application and background, but it gets you "doing calculus" very quickly and in a way that made a lot of sense to me as a a visual thinker. The edition I checked out from my high school library back in 1995 had practice problems with answers in the back. I hear there's a revised version out now; I'd be suspicious of it — Thompson's tone and style was such an integral (*groan*) part of the book that I'm guessing any kind of revision would only subtract from it. "What one fool can do, another can."
posted by msittig at 8:25 AM on December 17, 2009 [2 favorites]
posted by msittig at 8:25 AM on December 17, 2009 [2 favorites]
I like W. Micheal Kelley's The Humongous Book of Calculus Problems. The title speaks for itself. There are TONS of problems worked through step-by-step with explanations.
posted by handabear at 8:32 AM on December 17, 2009
posted by handabear at 8:32 AM on December 17, 2009
jeb: Spivak is really heavily aimed at future mathematicians. I loved loved loved it, but I would not recommend it to anyone who explicitly says they don't want one with that sort of bent.
posted by dorque at 8:51 AM on December 17, 2009
posted by dorque at 8:51 AM on December 17, 2009
My high scool AP text was Calculus and Analytical Geometry by Edwards and Penny. Lots of pictures and answers for half of the problems.
posted by chairface at 8:55 AM on December 17, 2009
posted by chairface at 8:55 AM on December 17, 2009
Some years ago when my partner was returning to school, he used the book Forgotten Calculus to brush up.
posted by not that girl at 9:07 AM on December 17, 2009
posted by not that girl at 9:07 AM on December 17, 2009
I used the Stewart book too, but I actually found the explanations and demonstrations at Visual Calculus more helpful to my comprehension.
BTW, I think Feynman actually taught himself from this book.
posted by borges at 9:34 AM on December 17, 2009
BTW, I think Feynman actually taught himself from this book.
posted by borges at 9:34 AM on December 17, 2009
I also used Stewart's book for first and second semester freshman year calculus. I liked it a lot and used to joke about sleeping with it. Solution manuals are available for your self-teaching.
posted by bread-eater at 9:43 AM on December 17, 2009
posted by bread-eater at 9:43 AM on December 17, 2009
Rather than trying to find the one true text book, I would peruse "iTunes U" calculus classes until you find one you like, then get the book that goes with that. Or, instead of iTunes, maybe MIT open courseware. You can do the work at the speed you like, but still get a real person (on video) explaining things. I'm not sure this is the path I'd take if I were learning calculus for the first time, but I recently watched a powerpoint with audio of basic calc on iTunes from an instructor at University of Arizona, and it was pretty good for a refresher.
posted by ctmf at 9:55 AM on December 17, 2009
posted by ctmf at 9:55 AM on December 17, 2009
borges, it appears you are right. There are lots of claims for "calculus made easy" on the internet, but only concrete evidence for "calculus for the practical man."
posted by msittig at 9:56 AM on December 17, 2009
posted by msittig at 9:56 AM on December 17, 2009
dorque: Ahh, that makes sense. I never actually used Spivak, just remembered people raving about it. But I guess I should have also tempered that memory with the memory that a lot of my friends are huge math nerds.
On the MIT OpenCourseWare idea, I think OCW has a lot of promise, but so far, my experience with it has been less than great. I've tried two courses from it (bio and chem), and the problem is, a lot of times the videos don't have the slides. Generally, its due to copyright issues. I imagine this is likely to be way less of a problem in calc, but so far, its been frustrating to get through two lectures, then the third one, when it starts getting interesting, every two minutes the screen goes black and you have no idea what the professor is talking about.
The other problem with iTU/MIT OCW idea is that intro calc is generally taught by grad students who have no interest in teaching the material, and are also highly probably to have nearly incomprehensible accents. At my school, even the advanced-track calc classes were taught this way. You had to go to super-double-crazy honors calc to get the prof who actually wanted to teach the material.
posted by jeb at 10:22 AM on December 17, 2009
On the MIT OpenCourseWare idea, I think OCW has a lot of promise, but so far, my experience with it has been less than great. I've tried two courses from it (bio and chem), and the problem is, a lot of times the videos don't have the slides. Generally, its due to copyright issues. I imagine this is likely to be way less of a problem in calc, but so far, its been frustrating to get through two lectures, then the third one, when it starts getting interesting, every two minutes the screen goes black and you have no idea what the professor is talking about.
The other problem with iTU/MIT OCW idea is that intro calc is generally taught by grad students who have no interest in teaching the material, and are also highly probably to have nearly incomprehensible accents. At my school, even the advanced-track calc classes were taught this way. You had to go to super-double-crazy honors calc to get the prof who actually wanted to teach the material.
posted by jeb at 10:22 AM on December 17, 2009
If you've taken calc already and just want to brush up, why not just pick up an AP Calculus BC review book? Get one from the library first and if you think it's any good, buy it. Heck of a lot cheaper than a textbook, but with lots of practice problems and generally good explanations.
I reviewed for the calc AP exam with a Princeton Review book. I thought it was excellent. Stewart is also good (I took multivariable calculus with it, so I got the thin "end of the book" book but thought it was clear and well written) but PR books would be like 1/5th the price or less.
posted by crinklebat at 10:31 AM on December 17, 2009
I reviewed for the calc AP exam with a Princeton Review book. I thought it was excellent. Stewart is also good (I took multivariable calculus with it, so I got the thin "end of the book" book but thought it was clear and well written) but PR books would be like 1/5th the price or less.
posted by crinklebat at 10:31 AM on December 17, 2009
but PR books would be like 1/5th the price or less
If you check Bigwords.com, a lot of times you can find international editions of textbooks for like 75% less than their amazon prices.
posted by jeb at 10:49 AM on December 17, 2009
If you check Bigwords.com, a lot of times you can find international editions of textbooks for like 75% less than their amazon prices.
posted by jeb at 10:49 AM on December 17, 2009
I was a quant in a past life. Are you sure statistics isn't what you want?
posted by joshu at 12:02 PM on December 17, 2009
posted by joshu at 12:02 PM on December 17, 2009
This was my college textbook for Calculus: Calculus (8th Ed.) by Larson, Hostetler, & Edwards
I really, really think this is the book you are looking for. I couldn't understand my Calculus instructors, so I was self-taught by this book; the quality of the text allowed me to get A's in Calc I, II, & III. Solutions to every odd problem are available for free on the text's website, so there's no need to shell out for any solution guides. (Also, IMO, this book is better than Stewart's Calculus text.)
I can't speak highly enough about this textbook.
posted by capitalist.pig at 1:47 PM on December 17, 2009 [1 favorite]
I really, really think this is the book you are looking for. I couldn't understand my Calculus instructors, so I was self-taught by this book; the quality of the text allowed me to get A's in Calc I, II, & III. Solutions to every odd problem are available for free on the text's website, so there's no need to shell out for any solution guides. (Also, IMO, this book is better than Stewart's Calculus text.)
I can't speak highly enough about this textbook.
posted by capitalist.pig at 1:47 PM on December 17, 2009 [1 favorite]
Also, I think you have the right approach going with a textbook. To understand Calculus, you need, more than anything, to work through problems. Work through as many problems as you can. The more you do, the greater your mastery will be.
posted by capitalist.pig at 1:54 PM on December 17, 2009
posted by capitalist.pig at 1:54 PM on December 17, 2009
Response by poster: Thanks for all the answers! Will review all of these.
As to the question about stats: my stats knowledge is sufficient at this point, though it could be enhanced, and I may decide to enhance it down the road.
posted by dfriedman at 2:55 PM on December 19, 2009
As to the question about stats: my stats knowledge is sufficient at this point, though it could be enhanced, and I may decide to enhance it down the road.
posted by dfriedman at 2:55 PM on December 19, 2009
I might also suggest going to the library to see whether they have any books that especially appeal to you. If you see something you like, you can order a copy for your bookshelf at home.
Also: after hearing a very cool, geeky, smart homeschooling dad rave about Saxon math, I finally got my hands on one of the Saxon algebra books. The philosophy is to aim for complete mastery, reinforcing previously-learned material constantly throughout the lessons, but what I really love is the whimsical wording of the practice questions:
posted by kristi at 5:33 PM on December 19, 2009
Also: after hearing a very cool, geeky, smart homeschooling dad rave about Saxon math, I finally got my hands on one of the Saxon algebra books. The philosophy is to aim for complete mastery, reinforcing previously-learned material constantly throughout the lessons, but what I really love is the whimsical wording of the practice questions:
Rockabilly was old hat, but some of the fans still enjoyed it. There were 29,000 fans at the festival, and 3000 of them were rockabilly fans. What fraction of the fans were rockabilly fans?Saxon Calculus is available at the Saxon homeschool store; you can probably find some copies at Amazon and various used outlets if you look.
A harsh law is called a "draconian" law after the Greek law-giver Draco. Two fifths of the laws were draconian. If 42 laws were draconian, how many laws were there in all?
Three sevenths of the cherubs had angelic faces. If there were 420,000 cherubs in the firmament, how many did not have angelic faces?
The ratio of chimeras to gargoyles is 2 to 11. If there is a total of 380 chimeras, what is the total number of gargoyles?
posted by kristi at 5:33 PM on December 19, 2009
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Calculus help .com
and
Calculus.org
They seem full of links and the like. Maybe you can find what you are looking for. Have fun I guess.
posted by Mastercheddaar at 7:14 AM on December 17, 2009