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I plan to record lectures for a MOOC on Calculus sometime next year. The MOOC is targeted at an undergraduate audience that comprises engineers, math majors as well as majors in the sciences, etc. They are all first year students. All students would have seen one variable calculus in quite some detail in high school. See here to get an idea of what students learn in school:

https://ncert.nic.in/textbook.php?lemh1=ps-6

https://ncert.nic.in/textbook.php?lemh1=ps-7

The course I am planning is a one year, two semester course (roughly 70-80 hours of recorded lectures) covering the standard topics of one variable calculus, sequences and series, multivariable calculus and vector analysis. Note that I have full control over the syllabus. I am unsatisfied with the presentation in the commonly used Calculus texts like Thomas's Calculus. I am looking for the following features in a textbook:

  1. The books should be of reasonable length and not be 1000+ pages. Something around 600-700 pages would be preferable.
  2. The book should not be an analysis textbook! The books need only give heuristic and physical or geometric arguments and proofs are not necessary except for the easier theorems.
  3. The books should not have 50 exercises for each section. I believe that solving 5 well-chosen exercises per section is better than solving 50 exercises most of which are minor variants of each other.
  4. It is okay if the book does not have many applications. All the students who take the course will be doing courses in physics and chemistry simultaneously so they will see plenty of applications anyway.
  5. The book should be relatively stable in the sense that there should not be a new edition in the next 4-5 years. The videos will be recorded only once whereas the same recorded lectures will be rerun in several iterations of the course. It would be helpful if the recommended book for the course remains in print for at least the next 5 years.

The books that I have found that satisfy all my requirements are the two calculus books by Lang (Short Calculus and Calculus of Several Variables). There is one more: Single and Multivariable Calculus by David Guichard et al. which has a bonus of being open source.

Are there more books that fit my requirements? If not, I will choose from the books above.

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    $\begingroup$ OpenStax? Hoffman? (Both open source.) $\endgroup$ – Sue VanHattum Dec 21 '20 at 23:00
  • $\begingroup$ @Sue Both books are much too long! $\endgroup$ – Jaikrishnan Dec 22 '20 at 16:25
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    $\begingroup$ You can take stuff out, as they are open source. If you don't find anything better. Does it matter how long it is, if students are using a pdf? $\endgroup$ – Sue VanHattum Dec 22 '20 at 16:44
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    $\begingroup$ I don't really understand the demand for few exercises. It's much easier to do less exercises than more, no? Even though your students will have had some good exposure to basic calculus, it strikes me as unreasonable to assume they'll never benefit from repetitive practice on some of the topics that will be new to them. $\endgroup$ – Kevin Arlin Dec 27 '20 at 1:50
  • $\begingroup$ 600-700 pages is not a reasonable length either. $\endgroup$ – Dan Fox Jan 15 at 12:15
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I would recommend Balmohan Limaye textbooks as it fits all your demands. The books are A Course in Multivariable Calculus and Analysis and A Course in Calculus and Real Analysis, both by Ghorpade & Limaye.

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    $\begingroup$ Answers with this little detail are not very useful. If you include a more in-depth explanation your answer will be better-received. $\endgroup$ – Chris Cunningham Dec 25 '20 at 22:08
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    $\begingroup$ @ChrisCunningham But doesn't the answer say everything it needs to? The question itself is highly specific and includes all the relevant details, so why repeat them? $\endgroup$ – Thierry Dec 26 '20 at 15:47
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    $\begingroup$ Thanks for editing @JW $\endgroup$ – Aditya Dwivedi Dec 31 '20 at 5:41

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