Exploring Calculus: Spivaks' & Apostols' Books & Experiences

In summary, the conversation is about two calculus textbooks, Spivak's Calculus and Apostol's Calculus, and which one is better for learning calculus in a rigorous manner. One person recommends Apostol's Calculus because it is used at Caltech and has a website with questions and solutions. Another person shares their experience with Apostal's Calculus, stating that it is very proof-driven and gives a unique perspective on the subject. They also mention that understanding Apostal's Calculus can give a deeper understanding of calculus compared to traditional methods. The conversation also briefly mentions Spivak's Calculus and its theoretical approach.
  • #1
torquerotates
207
0
Hi this question is for all you math people out there. But as you will find shortly, its very specific. I'm interested in learning calculus deeply. I learned nothing in the watered down calculus that is so readily offered because of the disenchantment with "Ivory tower education". But anyways. I'm still in the process of descideing between two supposibly excellent books that treats calculus in a rigorous manner. Spivaks' Calculus and Apostals' Calculus. Did anyone have positive experiences with any of these two? What was frustrating about going through these books? Did you gain anything that you wouldn't have if you just went to traditional route to real analysis?

On a side note: I noticed that all of Spivak's problems are out there in the form of a solutions manual. Can the same be said of Apostol?
 
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  • #2
defiantly go with apostal, It is really dense but if you can learn calculus from that textbook than you can learn it from any other. It is also used at caltech and here is the website that has questions and solutions to the things that were taught in class. I would suggest that if you do go with apostal then try doing these assignments. lol and i cannot find the link but when i do i will post it on here for you
 
  • #3
I took calculus from Apostal. It was a kick in the nuts for my first college math course. Apostal is unique because it starts out with integration and is very proof driven. I think it gives you a nice perspective of what Calculus can be. It was a perspective I wouldn't have until I took advance calculus a few years later. I noticed that taking calculus with theory gave me a leg up on everyone else who did not.

If you can work through Apostal and understand a good deal that he is saying, you will know more about calculus than most people. Even now as I look through the book again, I find new bits and pieces of information that make things become more clear.

I can't speak to much for Spivak, I never read it, but I hear it's good and more theoretical than Apostal (hard to imagine.)
 

1. What is the difference between Spivak's and Apostol's books on Calculus?

Both Spivak's and Apostol's books provide comprehensive coverage of Calculus topics, but they differ in their approach. Spivak's book is more rigorous and emphasizes proofs and theoretical concepts, while Apostol's book is more focused on applications and problem-solving techniques.

2. Are these books suitable for beginners?

These books are typically used in advanced undergraduate or graduate level courses, so they may not be suitable for beginners. However, they can be a valuable resource for motivated and dedicated students who are willing to put in the effort to understand the material.

3. How can these books help in understanding Calculus better?

Both Spivak's and Apostol's books provide a deep understanding of Calculus concepts through rigorous proofs and clear explanations. They also include many challenging exercises that can help improve problem-solving skills and strengthen understanding of the material.

4. How do these books compare to other popular Calculus textbooks?

Spivak's and Apostol's books are often considered more advanced and rigorous compared to other popular Calculus textbooks like Stewart or Thomas. They are also more focused on theoretical concepts rather than applications, so they may be better suited for students interested in pursuing higher level mathematics.

5. Can self-study with these books be effective?

Self-study with these books can be effective for motivated and dedicated students who have a strong foundation in mathematics. However, it is recommended to also seek guidance from a teacher or tutor who can provide additional support and clarification when needed.

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