Should Apostol's calculus be supplemented with Courant/Spivak

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In summary, the conversation discusses the best approach for studying Calculus and Real Analysis. The individual is currently studying from Apostol's book and is wondering if they should supplement it with other books such as Courant's or Spivak's. They mention facing difficulties in regaining their flow after a month-long gap and ask if they should start from the beginning or use a different book. The expert suggests that studying straight from Spivak's Calculus should be sufficient and that there is no need to read Courant's or Spivak's if they have mastered Apostol's book. They also suggest reading previous chapters to refresh one's memory if they are stuck.
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capsicum
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Hello ,
I am currently studying from the book Calculus - Volume 1 by Apostol . I am doing it as a pre cursor to studying Real Analysis by Rudin.

I am currently on the second chapter of the book. I am solving the exercises as best as I can.
My question is , while I am doing this book is it necessary to supplement it with a book such as 'Introduction to calculus and Analysis' by Courant or Spivak's Calculus. I usually don't face any difficulties in understanding the material from Apostol.

What has happened is that there has been a 1 month gap since I studied it last. And I am unable to gain the flow which I initially had with the book. This has happened because sometimes I have to refresh some of the older concepts. Should I restart the book from the beginning to regain the flow or should I use Courant's book to do those parts ?

Is it possible to approach Rudin after doing Apostol's book or one should also attempt Spivak/Courant before doing so?
 
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  • #2
My opinion is that you should study straight from Spivak's Calculus.
 
  • #3
Only doing Apostol should be enough. Spivak or Courant is on the same level as Apostol.
If you're stuck you should read previous chapters to refresh your memory.
 
  • #4
I agree with micromass. If you master and complete Apostol, there is no need to read Spivak or Courant.
 
  • #5


I cannot make a definitive statement on whether Apostol's calculus should be supplemented with Courant/Spivak. However, I can provide some insights and suggestions based on my knowledge and experience in mathematics.

Firstly, it is commendable that you are studying from Apostol's book as a pre-cursor to studying Real Analysis by Rudin. Apostol's book is a rigorous and comprehensive introduction to calculus and is widely used in mathematics courses. It covers all the essential topics and provides a solid foundation for further studies in mathematics.

In terms of supplementing Apostol's book with Courant/Spivak, it ultimately depends on your personal learning style and goals. Courant's book is more advanced and goes beyond the scope of traditional calculus, covering topics in analysis and differential equations. Spivak's book is also a rigorous introduction to calculus, with a focus on conceptual understanding and problem-solving techniques. Both books are highly recommended for further studies in mathematics.

Regarding the gap in your studies and the difficulty in regaining the flow, it is always helpful to review and refresh previous concepts before moving on to new material. This can be done by going back to the beginning of the book or using supplementary resources. It is also important to consistently practice and apply the concepts you have learned to solidify your understanding.

As for approaching Rudin's Real Analysis after Apostol's calculus, it is definitely possible. However, Rudin's book is more advanced and may require a deeper understanding of calculus and mathematical maturity. It may be helpful to supplement your studies with other books or resources, such as Courant/Spivak, to prepare for Rudin's book.

In conclusion, whether you choose to supplement Apostol's calculus with Courant/Spivak or not, the most important thing is to consistently practice and review the concepts you have learned. This will help you build a strong foundation in mathematics and prepare you for further studies in the field.
 

1. Should I study both Apostol's calculus and Courant/Spivak?

It depends on your goals and interests. Apostol's calculus focuses on a more rigorous and theoretical approach, while Courant/Spivak covers more practical applications. If you want a deeper understanding of calculus, it may be beneficial to study both.

2. Is one approach better than the other?

Both Apostol's calculus and Courant/Spivak have their strengths and weaknesses. It ultimately depends on your learning style and goals. Some may prefer Apostol's approach for its rigor, while others may prefer Courant/Spivak for its practical applications.

3. Can I supplement my calculus studies with both Apostol and Courant/Spivak?

Yes, you can certainly use both textbooks to supplement your calculus studies. This may give you a more well-rounded understanding of the subject.

4. Do I need to have a strong math background to understand these textbooks?

Both Apostol's calculus and Courant/Spivak assume a solid understanding of pre-calculus and basic algebra. It may be challenging for those without a strong math background, but with dedication and effort, it is possible to understand these textbooks.

5. Which one should I study first?

It is recommended to study Apostol's calculus first, as it provides a strong foundation in the theory and concepts of calculus. Courant/Spivak can then be used to supplement and reinforce the material learned from Apostol. However, this may vary depending on individual learning styles and preferences.

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