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I've studied calculus 2 years from Arabic text . It was great text , which is supported with huge amount of examples and exercises , Now , I find it's a good step to study the material in English as my future studies will be in English , So i search for a text which cover what I have learned before to learn English terminology and notation and so on , and then go further in the subject .

So , Do you know good text which start from the beginings of calculus - limits and derivatives - and then go through applications of derivatives and integrals and it's application in areas and volumes ? and also have series and further material in the subject .

My friends have recommended "early calculus transcendentals" by Ron Larson, and other recommended "essential calculus " for the same author .

How do you find those texts ? are there any other good texts ?

You have to notice that , I don't look for a text which go slowly throw the beginings , as I already have studied the subject before , but if the text go slowly the basics and also cover further subject , no problem with that.

Regards ...

FNH
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    Richard Courant's Introduction to Calculus and Analysis is a wonderful book on calculus. – A.E Jul 14 '13 at 15:55
  • Essential Calculus is a stripped down version which is definitely not suitable. – André Nicolas Jul 14 '13 at 15:57
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    I have three calculus books(Stewart's Calculus, 7e; Spivak's Calculus 4th ED.; and George B. Thomas. Jr's Elements of Calculus with Analytic Geometry.

    So far, Spivak's Calculus has been by far the most difficult text I've tried going through. It takes longer to complete, but through all the pain and rigour of studying Spivak(even though I'm only to Ch. 7), I feel an understanding unlike anything I've felt from other books.

    Stewart's Calculus 7e is a pathetic excuse for a mathematics book. Little to no proofs and a large disparity in exercise difficulty.

     – Jonathan Dewein Jul 14 '13 at 15:58
  • @AndréNicolas , what is essential calculus not suitable ? what about early calculus transcendentals ? it covers many subject like diffrenatial equations and series and many others . – FNH Jul 14 '13 at 16:00
  • Thomas Jr's Elements seems to be a great book thus far. Good exercises, good proofs, good focus on essentials and understanding without the blatant standardized test appease that is Stewart. – Jonathan Dewein Jul 14 '13 at 16:04
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    You know a lot already, and Essential Calculus covers a lot too few topics for your purposes. – André Nicolas Jul 14 '13 at 16:05
  • @AndréNicolas , alot too few topics ! this doesn't make sense to me! may you clarify ? , what about "early calculus transcendentals" , is it good ? – FNH Jul 14 '13 at 16:09
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    I am saying Essential Calculus is much too simple for you. Any of the big standard books will do for picking up English terminology. For mathematical quality, I would suggest stepping up to something like Apostol. But there is no shortage of decent books. – André Nicolas Jul 14 '13 at 16:15
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    Read Spivak, read Spivak. – Pedro Jul 14 '13 at 16:37
  • Does this answer your question? What are the recommended textbooks for introductory calculus? –  May 21 '23 at 23:45

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I think you'd do very well with Michael Spivak's Calculus. It's thorough, covers the basics, but so much more than that. His text is more rigorous and theoretical than are many texts used for introductory calculus. It is used in calculus courses, particularly those with a pure mathematics emphasis, at many universities. Spivak has also written The Hitchhiker's Guide to Calculus which reads more like a novel, and gives an intuitive understanding of Calculus. (He has said [somewhere?] that he has used it Hitchhiker as "supplemental reading" in the Calculus courses he's taught.)

An alternative but excellent and even more challenging text(s) would be to study Apostol's Calculus, Volumes I and II. This is more in line with the level of study for which I believe you are prepared.

I'm familiar with Stewart's Calculus - Early Transcendentals, and that will do just fine if your primary aim is to acquire proficiency in studying calculus in English. I just don't think it will challenge you as much as will Spivak's Calculus. Stewart also authors Essential Calculus, but it's just stripped down and not as enriching as is his other texts.

Remark: Given your previous coverage of Calculus and your study of Enderton and Dummit and Foote, I'd really suggest taking on Apostol's work. If not Apostol, go for Spivak. For both, you'll find lecture notes and syllabi to use to accompany the texts by Googling "Apostol, Calculus: edu" and checking our promising "hits".

amWhy
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  • So , can i say - as i have understood from your answer - that Calculus - Early Transcendentals by Larson and Sterwart teaches me methods in calculus , how to solve problems and apply the learnt methods throw applications and Spivak's text teachs me the theoretical prospective ? – FNH Jul 14 '13 at 16:25
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    You will learn applications with Spivak too. But you won't get a whole lot of theory with Larson and Stewart. I would say: "get them both", but Calculus texts are expensive! – amWhy Jul 14 '13 at 16:29
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    Let's just say that Stewart will teach you "how to do calculus computationally," while Spivak and Apostol will teach you "how to think about calculus, how to do calculus, and why what you're doing makes sense." I just think, given your level of inquisitiveness, that you'll be frustrated with Stewart and Larson. – amWhy Jul 14 '13 at 16:35
  • Yes , they are ! my friend has a hard copy of larson early calculus , he told me , I can borrow it as much as i want , so i just need one text - spavaik - .Do you have any idea about why are they expensive ? – FNH Jul 14 '13 at 16:39
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    Probably because of "demand"...lots of college students need to take Calculus, and oftentimes, for three semesters...Plus, textbooks are expensive, in general. – amWhy Jul 14 '13 at 16:40
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Fitzpatrick's book is the best, i think.

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A nice, out of print, but freely/legally downloadable 4-volume set on Calculus recommended by T.W. Körner is that by A.E. Maxwell available here. This reference by T.W. Körner comes from his new book Calculus for the Ambitious (I've only started reading it, but it looks nice, no surprise). He also recommends Spivak. I have both and they are both great. I have Apostol volume 1 and 2 also (1st and 2nd editions) and it is probably my goto, but I use them each from time to time.

Volumes 2-4 are available from the same site.

Joe
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