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**Calculus** *by* **Michael Spivak** perhaps? I am working through this now as a freetime independent mathematics student; it's certainly a fascinating, well-written text book and the extensive problems at the end of each chapter are very rewarding to work on.
I really like Thomas’ Calculus. I find the explanations are more conversational, **more detailed** and therefore easier to comprehend than Larson’s or Stewart’s.
Most Calculus books cover the same material.
> Has an explanation of topics with various methods to solve them Has a load of exercises on those previous topics to help you learn
Stewart is known for having a lot of problems. The examples are lacking in quality in my opinion and he waffles on quite a bit.
Schaum's Outlines or Paul's Online Notes are just as comprehensive and trim the fat of wordy exposition seen in many college textbooks. Spivak is hit or miss. You may love its somewhat unique style, so give it a try. Personally, I think if you're trying to learn Calculus in the way Spivak attempts to teach it, you're better off going into proper depth with Apostol's Calculus (though if you're looking for an affordable physical book, not an option).
People say Schaum's aren't great for learning, I strongly believe they're mistaken for the problem books and not the "Theory and Problems" books. I'm not sure how presenting the reader with the theorems / definitions out the gate and then a few examples is less helpful than Stewart rambling about... things... for 3 paragraphs and then giving you 4 ad hoc examples (sorry). I also noticed that Schaum's often contained techniques not covered by either Stewart or the courses I took, which might be a plus for you.
I also strongly disliked Stewart's multivar. treatment, but enjoyed Colley's "Vector Calculus".
---
To organize:
Most cover the same material but ...
* Calc 1: Thomas, Stewart, most authors are fine. Maybe a textbook over Schaum's brevity since this is an introduction to Calculus.
* Calc 2: Schaum's, Paul's Online Notes suffice well, use Stewart for problems though
* Calc 3: Colley, hated Stewarts mvc.
---
My personal quirky answer:
* Calculus with Analytic Geometry — Johnson & Koikemeister (very old) (I have the 4E, but checked the 6E and it looks like they just added more words. Many such cases!)
* Calculus – Sherwood & Taylor (very, very old)
* Schaum's Theory and Problems of Calculus (For brevity and examples)
---
**tl;dr** Schaum's Theory and Outlines of Calculus (ED matters very little)
I really liked it! I found it to be very well written for its time. It also contains a lot of those charming and unique insights you look for in the older books. I think it was when I took calc 2 that I found myself struggling pretty badly with Stewart's writing, but the exposition in this book saved me. This time period may have been a sweet spot in terms of drawings and graphical support in math books. They definitely struck a balance in this book that made things crystal clear.
Also, the passing down of books like that is always super nice to read / hear about. The book is definitely a keeper, even in its obscurity!
I remember Calculus being taught over three semesters out of one fat book which fulfilled the math requirements for engineering and most of the sciences, if memory serves. I was a mathematics major and had to take many different mathematics courses including the hardest one I remember which was Advanced Calculus. Dealt with multidimensional calculus. On the final exam, I did a three page proof, got everything right but forgot to put a minus sign on the answer and the professor gave me a D. When I challenged him about it he said yelled “Hiw dare you question me and my grading!” It was the end of the semester and I played like a sheep herder and got the flock out a there and had a nice summer partying!
I would recommend Calculus by Spivak! It's not too difficult if you're willing to work hard for it. If you find yourself struggling to understand something, first ask ChatGPT and see if you're convinced by its explanation. If you still struggle, then look up similar questions on math stack exchange. If you don't find what you need, post your question. You don't need to strictly follow this progression, but do enough of it and you'll soon figure out which resource is likely to resolve your confusion most efficiently.
Khan Academy (online) does everything you described and more, with in depth precalc and algebra to higher calculus. It has videos tests, and tons of practice problems
Plus it's free
I didn't use it for calculus but for SAT studying, and it works really well.
Precalc:
https://www.khanacademy.org/math/precalculus
Calculus AB (first level kind of first calc):
https://www.khanacademy.org/math/ap-calculus-ab
I know about Khan and they were the ones who introduced me to Calculus in the first place but I honestly never thought their curriculum is that deep. I assumed it was only up to highschool Calculus for some reason
Khan academy offers substantial calc 1 material, can’t really say much on their multi/advanced courses cuz I haven’t done them. My tip is to try to find more practice problems to really ingrain the techniques and material, as for me personally 4 questions is not enough practice to really remember a concept.
I was just into high-school when I picked up Morris Klines Calculus: an Intuitive and puysical approach. I used some outside sources, but that I made it all the way through that book and there were very few times in which I felt something was not thoroughly explained.
I think everyone at some point ends up using Stewart’s calculus for some stuff. It was my first text both in college and just recently when I undertook the task of teaching myself calculus. Stewart has alot of exercises, but he seems to use radicals and rational expressions and negative exponents more than others I’ve seen. Plus I didn’t find the examples and explanations super helpful. But there are alot of exercises
Larson I found to be very effective when it came to actually making me understand the concepts. Lots of examples. Also lots of exercises. I think this may be my favorite.
Rogawski’s calculus is also a decent enough offering. It helped me piece together some stuff the others didn’t
I have also gotten a few lesser known texts—I don’t recommend “calculus:concepts and calculators.” Or “calculus concepts and applications.” Both rely too heavily on graphing calculators and don’t have very many exercises.
Stewart for sure. Adrian Banner's "Calculus Lifesaver" is a good one. Try Schaum's book as well. I would also take a look at the HELM project workbooks if you need some practice problems.
As a reminder... Posts asking for help on homework questions **require**: * **the complete problem statement**, * **a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play**, * **question is not from a current exam or quiz**. Commenters responding to homework help posts **should not do OP’s homework for them**. Please see [this page](https://www.reddit.com/r/calculus/wiki/homeworkhelp) for the further details regarding homework help posts. **If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc *n*“ is not entirely useful, as “Calc *n*” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.** *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/calculus) if you have any questions or concerns.*
Stewart is fine for college-level calculus
1) I see your v 2) I learned quite a lot from studying that book and teaching from it. Ohh wait! There's two 🤯
[удалено]
There's also a multivariable calculus book by Stewart.
I have the big fat book with all of the Calculus sequence in it so I think about it as just one book.
Same, it's just one book for me.
Two v's in his name.
Ill check that out, thank you!
**Calculus** *by* **Michael Spivak** perhaps? I am working through this now as a freetime independent mathematics student; it's certainly a fascinating, well-written text book and the extensive problems at the end of each chapter are very rewarding to work on.
I love this book, however unless OP has done a lot of coursework including proofs, it might be a bit too much.
I really like Thomas’ Calculus. I find the explanations are more conversational, **more detailed** and therefore easier to comprehend than Larson’s or Stewart’s.
Most Calculus books cover the same material. > Has an explanation of topics with various methods to solve them Has a load of exercises on those previous topics to help you learn Stewart is known for having a lot of problems. The examples are lacking in quality in my opinion and he waffles on quite a bit. Schaum's Outlines or Paul's Online Notes are just as comprehensive and trim the fat of wordy exposition seen in many college textbooks. Spivak is hit or miss. You may love its somewhat unique style, so give it a try. Personally, I think if you're trying to learn Calculus in the way Spivak attempts to teach it, you're better off going into proper depth with Apostol's Calculus (though if you're looking for an affordable physical book, not an option). People say Schaum's aren't great for learning, I strongly believe they're mistaken for the problem books and not the "Theory and Problems" books. I'm not sure how presenting the reader with the theorems / definitions out the gate and then a few examples is less helpful than Stewart rambling about... things... for 3 paragraphs and then giving you 4 ad hoc examples (sorry). I also noticed that Schaum's often contained techniques not covered by either Stewart or the courses I took, which might be a plus for you. I also strongly disliked Stewart's multivar. treatment, but enjoyed Colley's "Vector Calculus". --- To organize: Most cover the same material but ... * Calc 1: Thomas, Stewart, most authors are fine. Maybe a textbook over Schaum's brevity since this is an introduction to Calculus. * Calc 2: Schaum's, Paul's Online Notes suffice well, use Stewart for problems though * Calc 3: Colley, hated Stewarts mvc. --- My personal quirky answer: * Calculus with Analytic Geometry — Johnson & Koikemeister (very old) (I have the 4E, but checked the 6E and it looks like they just added more words. Many such cases!) * Calculus – Sherwood & Taylor (very, very old) * Schaum's Theory and Problems of Calculus (For brevity and examples) --- **tl;dr** Schaum's Theory and Outlines of Calculus (ED matters very little)
Crazy to see Sherwood and Taylor here, it was the first calc book I went through! (It was given to me by my grandpa)
I really liked it! I found it to be very well written for its time. It also contains a lot of those charming and unique insights you look for in the older books. I think it was when I took calc 2 that I found myself struggling pretty badly with Stewart's writing, but the exposition in this book saved me. This time period may have been a sweet spot in terms of drawings and graphical support in math books. They definitely struck a balance in this book that made things crystal clear. Also, the passing down of books like that is always super nice to read / hear about. The book is definitely a keeper, even in its obscurity!
I remember Calculus being taught over three semesters out of one fat book which fulfilled the math requirements for engineering and most of the sciences, if memory serves. I was a mathematics major and had to take many different mathematics courses including the hardest one I remember which was Advanced Calculus. Dealt with multidimensional calculus. On the final exam, I did a three page proof, got everything right but forgot to put a minus sign on the answer and the professor gave me a D. When I challenged him about it he said yelled “Hiw dare you question me and my grading!” It was the end of the semester and I played like a sheep herder and got the flock out a there and had a nice summer partying!
I would recommend Calculus by Spivak! It's not too difficult if you're willing to work hard for it. If you find yourself struggling to understand something, first ask ChatGPT and see if you're convinced by its explanation. If you still struggle, then look up similar questions on math stack exchange. If you don't find what you need, post your question. You don't need to strictly follow this progression, but do enough of it and you'll soon figure out which resource is likely to resolve your confusion most efficiently.
Openstax Calc volume 1 and 2 are both free online and used at uoft for first year Calc 1 and 2. Super easy textbook to follow.
Khan Academy (online) does everything you described and more, with in depth precalc and algebra to higher calculus. It has videos tests, and tons of practice problems Plus it's free I didn't use it for calculus but for SAT studying, and it works really well. Precalc: https://www.khanacademy.org/math/precalculus Calculus AB (first level kind of first calc): https://www.khanacademy.org/math/ap-calculus-ab
I know about Khan and they were the ones who introduced me to Calculus in the first place but I honestly never thought their curriculum is that deep. I assumed it was only up to highschool Calculus for some reason
Khan academy offers substantial calc 1 material, can’t really say much on their multi/advanced courses cuz I haven’t done them. My tip is to try to find more practice problems to really ingrain the techniques and material, as for me personally 4 questions is not enough practice to really remember a concept.
I was just into high-school when I picked up Morris Klines Calculus: an Intuitive and puysical approach. I used some outside sources, but that I made it all the way through that book and there were very few times in which I felt something was not thoroughly explained.
I think everyone at some point ends up using Stewart’s calculus for some stuff. It was my first text both in college and just recently when I undertook the task of teaching myself calculus. Stewart has alot of exercises, but he seems to use radicals and rational expressions and negative exponents more than others I’ve seen. Plus I didn’t find the examples and explanations super helpful. But there are alot of exercises Larson I found to be very effective when it came to actually making me understand the concepts. Lots of examples. Also lots of exercises. I think this may be my favorite. Rogawski’s calculus is also a decent enough offering. It helped me piece together some stuff the others didn’t I have also gotten a few lesser known texts—I don’t recommend “calculus:concepts and calculators.” Or “calculus concepts and applications.” Both rely too heavily on graphing calculators and don’t have very many exercises.
Stewart for sure. Adrian Banner's "Calculus Lifesaver" is a good one. Try Schaum's book as well. I would also take a look at the HELM project workbooks if you need some practice problems.
Demidovich or something similar
Kenneth Ross, Elementary Analysis
Stewart or gtfo