Which Calculus Textbook is Right for Me?

In summary, there are many rigorous calculus texts available, and both Spivak's and Courant's books are highly recommended.
  • #1
randommanonea
7
0
Hello,
Can anybody help me by recommending a rigorous calculus textbook.
I have done some parts of Thomas's Calculus and the questions in it are mainly computational (plug and chug type).
I want a book which is both rigorous and has good quality questions.

I have selected two books-
1.) Calculus by Spivak
2.) Introduction to calculus and analysis by Courant
Which is better ?
 
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  • #2
From reading both, I deduced that Spivak learned from Courant, and wrote a more modern, more theoretical version. It doesn't hurt to have both of those, or whatever ones budget allows. Spivak is lots of fun and extremely well written. Courant is also very well written in a more classically scholarly and serious tone.

the difference in terms of content is that courant has a more applied flavor and spivak is completely pure. E.g. there are more differential equations in courant.

the theoretical tone is also a little different since courant was written in the 30's and 40's and uses concepts like "accumulation points" while spivak was written in the 60's and uses slicker "least upper bound" axioms.unfortunately the days when i bought courant for $6.75 are gone, and it sells new now for over $100. so i recommend getting instead a copy of the rewrite by fritz john, by courant and john, as almost he same, maybe mathematically a little better or at least more modern, and often much cheaper.

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Introduction to Calculus and Analysis, Vol. II/1 (Classics in Mathematics) (ISBN: 3540665692 / 3-540-66569-2)
Richard Courant; Fritz John
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I have replaced my original link to an international edition with this one costing $5 more, since I am philosophically opposed to international editions which to me are to some extent illegal or at least immoral when purchased in the USA.
 
Last edited:
  • #3
Either of these books would be well supplemented by either of Professor Binmores' offerings

Mathematical Analysis
Calculus

These are much more modern treatments.



Advanced Calculus by Buck is also good and dates between Spivak and Binmore.

go well
 
  • #4
From reading both, I deduced that Spivak learned from Courant, and wrote a more modern, more theoretical version. It doesn't hurt to have both of those, or whatever ones budget allows. Spivak is lots of fun and extremely well written. Courant is also very well written in a more classically scholarly and serious tone.

the difference in terms of content is that courant has a more applied flavor and spivak is completely pure. E.g. there are more differential equations in courant.

the theoretical tone is also a little different since courant was written in the 30's and 40's and uses concepts like "accumulation points" while spivak was written in the 60's and uses slicker "least upper bound" axioms.unfortunately the days when i bought courant for $6.75 are gone, and it sells new now for over $100. so i recommend getting instead a copy of the rewrite by fritz john, by courant and john, as almost he same, maybe mathematically a little better or at least more modern, and often much cheaper.

Stock Image
Introduction to Calculus and Analysis, Vol. II/1 (Classics in Mathematics) (ISBN: 3540665692 / 3-540-66569-2)
Richard Courant; Fritz John
Bookseller: BEST BARGAIN BOOKS
(EAST PATCHOGUE, NY, U.S.A.)

Bookseller Rating:
Quantity Available: 4
Book Description: Springer. Book Condition: New. New, unread, unused and in perfect condition. Bookseller Inventory # 2-BT-13-01-939

Bookseller & Payment Information | More Books from this Seller | Ask Bookseller a QuestionPrice: US$ 25.44
Convert Currency
Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds
\
I have replaced my original link to an international edition with this one costing $5 more, since I am philosophically opposed to international editions which to me are to some extent illegal or at least immoral when purchased in the USA.there are also free smsg books that have more rigor than most texts today:

http://www.eric.ed.gov/ERICWebPorta...RICExtSearch_SearchValue_0="Herriot+Sarah+T."
 
Last edited:
  • #5
Anyone have the solutions manual for spivak's 3rd edition? or tell me where to buy/find it? There doesn't seem to be one. Thanks
 

1. What level of mathematics is required for a calculus textbook?

Most calculus textbooks assume that the reader has a strong foundation in algebra and trigonometry. Some may also require knowledge of pre-calculus concepts such as limits and basic functions.

2. Are there any differences between high school and college level calculus textbooks?

Yes, the main difference is typically the depth and complexity of the material covered. College level textbooks may also assume a higher level of mathematical maturity and have more challenging exercises.

3. How do I know if a particular textbook is suitable for my learning style?

It is important to preview the textbook and see if its format, examples, and explanations align with your preferred learning style. Some textbooks may also have online resources or supplementary materials that can cater to different learning styles.

4. Can I use an older edition of a calculus textbook?

In most cases, yes. However, it is important to check with your instructor to make sure the older edition covers the same material as the current edition. There may also be slight differences in notation and exercise numbers between editions.

5. How do I compare different calculus textbooks?

Some factors to consider when comparing calculus textbooks include the level of difficulty, the depth and breadth of topics covered, the clarity of explanations and examples, the availability of online resources, and the cost. It may also be helpful to read reviews or ask for recommendations from peers or instructors.

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