Calculus resources for the curious?

September 10, 2006 8:02 PM

I would like to relearn some calculus on my own. Please recommend the best book for the purpose.

It is embarrassing to me that I presently lack the math required to properly grasp basic Newtonian physics. I would like to regain competency equivalent to what is gained over the course of a year or two of college-level calculus.

Please point me in the direction of a great (text)book that will get me started. Clarity and concision are a must.

Tangentially, I'm also curious as to what topics are usually covered in two years of calculus classes.

posted by perissodactyl to science & nature (16 answers total)

The sequence as I was taught it/will be taught it goes single-variable differential, single-variable integral, insanely basic differential eqs, multivariate differential, multivariate integral, differental eqs, partial differential eqs.

This old thread of mine has a list of the recommended calc books.

In addition, depending on what you're doing, learning it with infinitesimals instead of limits can be more intuitive at first. This online book is a good introduction to calculus with infinitesimals. Probably wouldn't be bad to look at that briefly, at least.
posted by devilsbrigade at 8:14 PM on September 10, 2006 [1 favorite]

That sequence, btw, was one year of highschool calculus and 3 quarters of multivariable calculus.
posted by devilsbrigade at 8:15 PM on September 10, 2006

The best calculus book of all time is Michael Spivak's Calculus. Clarity and concision are its strong suits, but be warned: its lack of fluffyness makes it too difficult for the non-committed.
posted by iconjack at 8:20 PM on September 10, 2006 [1 favorite]

In most of the course series Ive seen, calculus is usually divided into 3 semester long courses-- calc 1: derivatives; calc 2: integration; and calc 3, vector calculus.

I don't really have a good recommendation for covering the first two; as most intro college textbooks try to be everything to everyone, they mutate quickly into encyclopedic monstrosities. However, once you've covered the material in the first two courses, Div, Grad, Curl and all that is a classic for its intuitive and concise coverage of vector calc.
posted by Maxwell_Smart at 8:20 PM on September 10, 2006

What level of rigor are you interested in?
posted by mr_roboto at 9:23 PM on September 10, 2006

Paul Dawkins, a professor at Lamar University, has a series of comprehensive class notes correspond with courses using Stewart's Calculus: Early Transcendentals. The book isn't very good but the notes, examples, and graphics he uses are fantastic.
posted by djb at 10:17 PM on September 10, 2006 [1 favorite]

I am in college, doing exactly what you describe. Ian Stewart's books are standard around here, and I like them compared to the one or two others I've used.
posted by phrontist at 10:30 PM on September 10, 2006

Calculus: Early Trancendentals? What's that? Apparently, it's different from the same author's Calculus, which I think would be an excellent choice. In addition to being an excellent calculus text, it includes several asides which cover applications. One of them is a derivation of the laws governing planetary orbits.
posted by stuart_s at 10:33 PM on September 10, 2006

Er... specifically, it start's with Newton's laws of motion and his law of universal gravitation and uses the techniques of calculus to derive Kepler's laws of planetary motion. It also has a lengthy discussion of Maxwell's laws of electromagnetism which I'm going to read Real Soon Now.

Spivak is another excellent calculus book but it has less in the way of exposition and relies on the reader to develop the techniques in the excercises. I also think it has less explicit discussion of applications.
posted by stuart_s at 10:45 PM on September 10, 2006

I vote for "Calculus: the Easy Way". Unlike the books that were recommended earlier it wasn't designed to be used in conjunction with a calc course, bur rather for self-teaching. The book follows a bit of a fantasy narrative (I swear it's not lame) where the characters in a kingdom are forced to use calculus to solve the various problems they face. It is very straight-forward, actually, and there are plenty of practice exams and math-y explanations. But the narrative makes a generally difficult subject much easier to digest.

I wouldn't say that the book (or any book) could truly bring you up to the level of an advanced calc student, but it will get you started, and will give you the confidence and the core knowledge needed to attack advanced calc texts.
posted by apple scruff at 11:05 PM on September 10, 2006 [1 favorite]

Arghhh! I have confused my calculus textbooks. The author isn't Stewart. It's Simmons. It's a good text and everything else I said above is accurate. I checked.
posted by stuart_s at 11:18 PM on September 10, 2006

I'd seccond a reccomendation for Spivak. The man knows his stuff.
posted by vernondalhart at 12:09 AM on September 11, 2006

I like Calculus Made Easy by Silvanus Thompson.
posted by baho at 5:11 AM on September 11, 2006

Oh yeah Spivak. Then after you've got the basics, while the calculust is still upon you, you can transition straight into Comprehensive Introduction to Differential Geometry!
posted by rlk at 7:21 AM on September 11, 2006

perissodactyl,

How fast do you want to learn? What specific things do you hope to analyze? Is it really calculus that interests you, or just math in general? Do you feel somehow inadequate in your work because you have things to analyze that you can't because you feel you lack the tools?

Or are you just really interested in learning basic Newtonian physics?

How long ago was it that you felt competent in this area and is a 'refresher' perhaps all you need?

Do you feel competent in geometry, trig, and algebra? Or do they need work, too?

Lots of questions, I know, but any recommendation above presumes answers that may not be relevant to your specific needs. (Feel free to drop me an email (in my profile)).
posted by FauxScot at 7:52 AM on September 11, 2006

What an interesting thread -- I'm currently doing the same thing (only I'll be taking a university calculus course in a few weeks). At the moment I'm brushing up on precalc, and as such haven't gotten into too much calculus; however, many people have recommended Hurricane Calculus, and in a preliminary read I enjoyed Silvanus Thompson's Calculus Made Easy (as recommended by baho).

My class is using Calculus by Varberg, Purcell, and Rigdon. Although the 9th edition is currently unrated on Amazon, earlier editions have received some favorable reviews. Of course, I can't comment on it myself, yet.
posted by penchant at 11:14 AM on September 11, 2006