In some cases, the decision may have already been made for you… The good news is that there’s no need to worry!īecause after teaching calculus for the past 15 years, I’m going to give you the best way to approach learning the material. I can give more recommendations of you would like.Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher) It gives a comprehensive overview of the history and development of calculus. This has plenty of unsolved problems from precalculus and algebra to more advanced topics.įor the history of calculus, as well as the book by Spivak mentioned above, I would recommend the history of the calculus and its conceptual development by Carl Boyer: I would also consider using the website Brilliant if you require a more basic foundation: They are also available in other maths topics, such as differential geometry and probability. It has huge numbers of solved and unsolved problems so I would definitely recommend that. It starts off with the absolute basics (about lines and circles) and ends up on advanced multivariable calculus.
BASICS OF CALCULUS FOR BEGINNERS SERIES
Take a look at it to see how badly written a mathematics book can be.Ĭhicago undergraduate mathematics bibliographyįor a textbook in calculus, I would recommend Schaum's outline series for calculus: This was the 150s text inġ994–95 it tries to give a Spivak-style rigorous presentation inĬolorful mainstream-calculus-book format and reading level. (the second volume includes multivariable calculus). Upper-level text: lemma-theorem-proof-corollary. This is “the other” modern rigorous calculus text. (Remember what Abel said about reading the They're old, and old books are hard to read,īut usually worth it. (including as much about Fourier analysis as you can do without Courant goes further into applications than is usual Hardyįocuses more on conceptual elegance and development (beginning byīuilding up R). They are classic treatments of theĬalculus, from back when a math book was rigorous, period. I haven't read it, but a lot of 130sĬourant, Differential and integral calculus Spivak, The hitchhiker's guide to calculus Other calculus books worthy of note, and why: Mathematical maturity and epsilonic technique that no math major To this book comes from tutoring and grading for 161, but I seriouslyīelieve that working as many problems as possible (it must beĪcknowledged that many of them are difficult for first year students,Īnd a few of them are really hard!) is invaluable for developing the
More advanced students who flip back through it? Most of my exposure Yes, it's good, although perhaps more of the affection comes from The best calculus book overall, and I've seen it do a wonderful job of Place of the words “compact” and “connected”).
Hard Theorems in chapter 8 (where a lot of epsilon-pushing takes the Sophistication at the expense of clarity, as in the proofs of Three Perhaps too few of them deal with applications (but you can find that The exercises get a little monotonousīecause Spivak has a few tricks he likes to use repeatedly, and I've seen (you can see throughout that Spivak has a vision of what The whole thing is the mostĬoherently envisioned and explained treatment of one-variable calculus Where I finally learned what a limit was, after three years ofīad-calculus-book “explanations”. Have the time, read it and do all the exercises. Of course, as we all know, the One True Calculus Book is Paul's Notes are really an instructive tutorial that allows you to proceed at your own pace, provides exercises, organizes the material into "modules" so you can work through and digest sub-sections/topics progressively. The link will take you to the Calculus I notes, but there's a menu at the top of the page where you can select notes for algebra/precalculus. I'll also provide a link to the Khan Academy, where you can review pre-requisite material, and supplement your journey through Calculus with video lectures, practice problems, etc.įinally, here is a link to Paul's Online Math Notes. You might enjoy this site that gives timeline of the history of calculus. And it outlines the development of Calculus, and the motivation for its development to some degree.
It won't replace a calculus textbook, but it really is great reading to understand calculus a bit more intuitively. That said, a very nice supplement to a textbook is Michael Spivak'sĪ Hitchhiker's Guide to Calculus. And if you want to learn calculus, you're going to have to have some sort of "textbook." And some are better than others. If you want to learn calculus, you should ensure you have mastered material typically covered in a Precalculus course.
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