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kremit

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In summary, the conversation revolved around recommendations for a calculus textbook with real-life examples. Suggestions were made for Larson, Strang, Keisler, Stewart, and Courant. Some individuals recommended Spivak, but others noted that it may be too advanced and abstract for someone looking for practical examples. It was also suggested to supplement a pure math book with a calculus-based physics book to strengthen applied skills. Dieudonné was mentioned as another option.

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kremit

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zonk

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kremit

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zonk

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Doesn't have pictures for most word problems. But I pretty much taught myself calculus from it having a very shoddy (reflecting back on it) high school math education. If you want to learn practical calculus, it's a good book, but it isn't for a person interested in theory--it omits a few proofs.

https://www.amazon.com/dp/061850298X/?tag=pfamazon01-20

Maybe it's because they bored me and I didn't do the repetitive problems, but I forgot most of the vector calculus covered in the book.

https://www.amazon.com/dp/061850298X/?tag=pfamazon01-20

Maybe it's because they bored me and I didn't do the repetitive problems, but I forgot most of the vector calculus covered in the book.

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BloodyFrozen

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Strang and Keisler are both good choices that also happen to be free.

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kremit

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bcrowell said:

Strang and Keisler are both good choices that also happen to be free.

I am mistaken. I thought this was a cluster of information with names of math types within catagories. CK12.org link on that website lead my to a 8 chp calculus book including youtube videos within it. That's pretty damn cool. Though I am not seeing any practicle examples in this book, i'll have to dive further. Thanks guys :)

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snipez90

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But seriously, if you want "real life" examples you should probably just stick to something like Stewart or Larson I guess. Also part of learning basic problem-solving skills in math is producing your own pictures for any given word problem.

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brocks

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snipez90 said:Yeah I second BloodyFrozen's recommendation since analysis is obviously better than calculus.

Be glad he didn't recommend Rudin.

To the OP: The reason most modern calculus texts are over a thousand pages is because they are full of examples and problems, way more than anyone person is likely to do. After basic drill problems, most of them are application problems that relate to the "real world." A cheap used edition of any of the mainstream texts, e.g. Stewart, Larson, Anton, Thomas, etc., will have all the examples you want. And as Dr. Crowell notes, there are excellent free resources on the web, including his own calculus book. You should also check out the free video lectures at MIT OCW and other sites.

Spivak is more appropriate for gifted math majors (like in MIT's honors calculus class) who have a professor to help them along.

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BloodyFrozen

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osnarf

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Also, while definitely not impossible, it's probably not best for a first course unless you are dedicated and in general have an aptitude for math, because the problems can be very taxing (and half of the information of each chapter is saved for the problem sets, so you can figure out the important results for yourself). Supposedly (I have not read it) Courant's calculus books are at the same general level as Spivak, but have more applications to physics (which is where you will see lots of real world examples). Again though, being at the same level as spivak might not be such a good thing for your first course unless you're ready for a challenge. Between the two, however, Courant seems more of what you were looking for, so if you wanted a more advanced textbook that would probably be your best bet.

I really don't like stewart so I personally wouldn't recommend that, and I haven't read any other single variable calc books all of the way through besides stewart and spivak, so I don't know of any book that would meet your requirements and be at an introductory level. However, a good course of action might be to learn calculus from a pure math book, and then work through a calculus based physics book, which will strengthen your applied calculus skills while simultaneously teaching you physics.

EDIT: If you go with Spivak or Courant, make sure you are very confident in your trig and calculus abilities, as this knowledge will be pretty much assumed. Also, it might be beneficial (but not 100% necessary) to read a book like "how to prove it" or some of ther math logic book first if you don't have any experience with proofs (and I don't mean the proofs from high school geometry).

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Sankaku

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snipez90 said:...analysis is obviously better than calculus.

Maybe we should all skip Spivak and just read Dieudonné? I am a big fan of Spivak but, as others have said, different books are good for different people.

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brocks

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- #14

jcw99

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brocks said:

The classic (1910) "calc for dummies" book is Calculus Made Easy by Thompson. He says in the introduction, "What one fool can do, another can." It's in the public domain, and you can get it for free on the web.

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fourier jr

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bcrowell said:The classic (1910) "calc for dummies" book is Calculus Made Easy by Thompson. He says in the introduction, "What one fool can do, another can." It's in the public domain, and you can get it for free on the web.

that's a classic, and for applications or real-world problems it's got to be either http://books.google.ca/books?id=YdjK_rD7BEkC"

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kremit

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bcrowell said:The classic (1910) "calc for dummies" book is Calculus Made Easy by Thompson. He says in the introduction, "What one fool can do, another can." It's in the public domain, and you can get it for free on the web.

The lack of orginization on the web makes me avoid it. The structure and orginization of a book is very exceptional. It teaches you without needing someone to guide you or explain things to you. Most of the math dummies books are good at breaking down problems, assisting you in solving the problem, but that is it.

I want practicle exams to be able to apply my knowledge to something. Something I want to create either through physical or programming. When I drilled through colleges courses up to trigonometry, I only know how to do problems on paper and not nessarly apply these problems to anything real. One or two AP classes at the university were good at this, but I cannot afford university classes.

Ironically the beginning chapters of triginometry i struggle with horribly, but after the intro, it comes easy. I feel it was because of careless mistakes.

I wish everyone would forgive my English. Though English is my first language, the older I get, the more my mind seems to go. I am only 29 years of age, which is strange. Again, I really appreciate everyone that has perticipated in this thread.

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mathwonk

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Vector Field

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I have read Stewart's book on Calculus and I think it does a fine job of introducing the material. It's a very introductory book, but I think it does the trick at explaining the basics. I've also read Thomas' book and while the level of detail may be slightly higher than Stewart's... something just rubbed me the wrong way when reading Thomas and I did not like the way things were explained very much.

Spivak's Calculus, which is more of an Analysis book (which I am reading now), is extremely rigorous and very well written. This is not a book to take on unless you understand mathematical proof already, as far as I can tell. In the first chapter he invokes concepts like induction. So, I am not sure how well this would fare for the average Calculus learner. Stewart's will certainly teach you the mechanics and maybe it is best to learn mechanics first and then delve deeper into the realms of analysis. This is how most schools do it anyway, I think. With Analysis first, you'd have to re-arrange some understanding in talking about the material. Or you could read "Discrete Structures" by Kenneth Rosen, which does not require Calc to know and will prepare you with Logic, Set Theory, and Proof techniques to take on Spivak.

I've read some others, but I did not find them impressive or worth mentioning much.

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brocks

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Vector Field said:Or you could read "Discrete Structures" by Kenneth Rosen,

Did you mean "Discrete Mathematics and Its Applications" by Rosen? I couldn't find "Discrete Structures" by that author.

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Vector Field

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brocks said:Did you mean "Discrete Mathematics and Its Applications" by Rosen? I couldn't find "Discrete Structures" by that author.

Yes, yes! Thank you for the error catch. I should have simply shifted books around on my desk to reference it correctly. We used it at my university in a course called "Discrete Structures". Sorry about the mistake.

The best calculus textbook for beginners depends on the individual's learning style and needs. Some popular options include "Calculus: Early Transcendentals" by James Stewart and "Calculus" by Michael Spivak.

It ultimately depends on personal preference and needs. Online textbooks offer convenience and often have interactive features, while physical textbooks allow for easier note-taking and highlighting. Some students may prefer a combination of both.

A regular calculus textbook covers the basics of calculus, including limits, derivatives, and integrals. An advanced calculus textbook delves deeper into the subject, covering topics such as vector calculus, multivariable calculus, and differential equations.

It is important to consult with your course syllabus and/or instructor to determine which textbook aligns with the course material. You should also consider your learning style and whether the textbook includes helpful resources such as practice problems and solutions.

Yes, there are many free online resources for calculus textbooks, including ebooks, PDFs, and interactive websites. Some popular options include "OpenStax Calculus" and "Paul's Online Math Notes."

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