I've been trying to educate myself in various areas of mathematics. I have been out of any formal math education for quite some time and so I brushed up on some basic (really, really basic) stuff including algebra and so forth. I'm working my way through some calculus and I'm using Michael Spivak's Calculus (4th ed.), which is fantastic, but I'm finding it to be a bit difficult at times. Do you have any recommendations for a good book or any other path that might make sense for someone without a very strong, formal background in math for learning calculus?
I should add that a major motivation in my renewed interest in math is related to my interest in applying it to computer science. I know that many will respond saying that calculus is, therefore, not the best place to spend my energies (discrete math might be better) and I'm sure that's a reasonable point, but I'm also interested in calculus per se. I guess there are a lot of areas in computer science where I feel like I'm lacking because I'm not competent with functions, etc, for example in algorithm analysis and big-O notation.
I realize this was a bit rambly and some of this might be totally off — if it is, it's from pure ignorance — and for that I apologize. I guess I'm just sort of confused as to where my energies would best be spent given my goals.
Best Answer
Gilbert Strang's Calculus. The best all purpose, general level calculus text bar none. Tons of applications, carefully and beautifully written and containing many applications and insights you simply won't find anywhere else.
And best of all,the first edition's available online for free.
That's the best one if you're not interested in a specific aspect of the subject.