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This question is a generalization of the common question asking for calculus references. It is here to abstract away the repetition, and give a canonical resource for calculus references.

I'm looking for a resources to learn single-variable calculus.

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Please add to the answer, and make this a canonical answer. –  mixedmath Aug 18 at 4:32

1 Answer 1

We break up this answer into a few different categories which partially overlap.

  1. Non-textbook resources.
  2. Supplemental Resources, which might try to give a bird's eye view, but doesn't give a complete course.
  3. Introductory resources, or what might usually be used in a first year of calculus in a university, usually where proofs do not form a large component of understanding.
  4. Rigorous calculus resources, usually with proofs.
  5. A note about "analysis."

Non-textbook resources

  1. The MIT OCW complete course, including video course lectures, lecture notes, homeworks with solutions, and exams with solutions. There are multiple versions of calculus on MIT OCW.

  2. The Khan Academy is a semi-complete course, with slow, complete guided overviews of computational problems encountered in first-year calculus. Many would argue that this is best used as a source of example problems with complete solutions, but others say it served as an adequate introduction to calculus.

  3. Paul's Online Math Notes form a complete resource, and are usually extremely easy to read. This is also a good resource for multivariable calculus and differential equations.

  4. Coursera has a few calculus courses, usually starting in spring and fall in time with the US university schedule. But Jim Fowler's Coursera course is always available, self-paced, comes with 15 hours of lectures and some supplementary materials. (He's working on a follow-up course covering series developments and a multivariable course too.)

Supplemental Resources

  1. Timeline of calculus.

  2. Spivak's The Hitchhiker's Guide to Calculus is widely considered a great overview of calculus for the beginner, though it is not a substitute for a textbook.

  3. Sawyer's What is Calculus About?

  4. Berlinski's A Tour of the Calculus is a verbose, introductory overview.

Further, google will yield a wide gamut of sources that people have written. Course lecture notes, supplementary materials, "intuitive introductions to calculus" and the like abound behind a google search.

Introductory Resources

Most "standard" calculus textbooks are isomorphic. They are more or less the exact same as each other. Most of these authors are mass-appeal, and have several versions, each with several editions. For self-study, there's little difference from edition to edition - different exercises, sometimes content updates. Books with "early transcendentals" in the title indicates that the book introduces trigonometric, exponential, and logarithmic functions early in the text. "Late transcendentals" means these functions are discussed later in the text. The most common books are

  1. Stewart's calculus books textbooks.

  2. Larson and Edwards's calculus books.

  3. Thomas's calculus books.

  4. Rogawski's calculus books.

  5. Leithold's calculus book.

  6. Varberg and Purcell's calculus book.

Rigorous calculus resources

  1. Spivak's Calculus is widely regarded as one of the best calculus books written. The Chicago Undergraduate Mathematics Bibliography, which is itself a great resource for finding math references, describes Spivak's Calculus as "The One True Calculus Book." It's important to note that much of the material is properly developed in the exercises, and even then some material is omitted that is included in other rigorous calculus resources.

  2. Apostol's Calculus, Volumes I and II are also widely loved, but are more difficult than Spivak. An interesting fact is that Apostol introduces integration first; closer to history, perhaps, but different than most modern presentation.

  3. Lang's A First Course in Calculus is dry, but without bloat.

  4. Fitzpatrick's Advanced Calculus is loved, but blurs the border between "calculus" and "analysis", and thus requires a good amount of mathematical maturity.

Mathematical Analysis

"Analysis" is a logical superset of calculus. The ideas in calculus are fully fleshed out, proved, based in logical foundations, extended, and generalized in analysis. But some authors use "calculus" and "introductory analysis" as synonyms, which can lead to some confusion.

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I have learned more about Calculus from this old one: Modern Calculus and Analytic Geometry. If you like, please add it to above. :-) –  Babak S. Aug 18 at 4:48
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Added the Louis Leithold reference ;) It's a nice book :) –  TX286 Aug 18 at 4:51
    
Here are some nice notes that supplement Spivak's Calculus: math.uga.edu/~pete/2400full.pdf –  nsanger Aug 18 at 4:58
    
I added another reference: Varberg and Purcell. I've learned with it :) –  TX286 Aug 18 at 5:10

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