Which books to go from calculus to analysis?

In summary, the conversation discusses the difficulty of reading Apostol's book on calculus and the individual's preference for starting with a high school calculus book. They also mention wanting to study advanced calculus and analysis, but are unsure which books to read. They consider reading the high school book first, then Schaum's Outline of advanced calculus, followed by Apostol's Analysis. However, they feel conflicted about not reading Apostol's first volume. The conversation concludes with a suggestion to first master the basics of calculus before moving on to advanced material.
  • #1
Jimmy84
191
0
I just finished doing pre calculus and I was eager to get started with calculus so I started to read apostol however the book happens to be somewhat dificult for me. It begins proving the exaustation method of Archimedes, and with other subjects, I preferred to start with my brother's high school calculus book which is way easier. I wonder which books should I get for advanced calculus and analysis. Is apostol v2 advanced calculus? I also have mcgraw hill schaums outline of advanced calculus which is 442 pages. I d like to read as less books as possible, In order to have more time to study more advanced math.

Im considering to read as fast as I can the high school calculus book, then to try schaums outline of advanced calculus and then apostol s analysis. but it 'd make me feel bad not to read apostol v1 and v2 a lot.

Any advices about which study plan to follow?
 
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  • #2
v2 of apostol is multivariable calculus its an extension of the first volume same style, so I am not sure what difference our looking for.
You can't do it all in a month, itl take some time to finish calculus both single and multi. Id recommend after that to then read apostol in you free time etc. in addition with a book on analysis. this i'll probably take more time as analysis is much more difficult to begin with
 
  • #3
You could probably get the basics of calculus down from a quick reading of the high school book, but once you know more or less what's going on take the time to read Apostol. If you want to understand advanced material, make sure you've got the basics down. Schaum's Outlines aren't bad, but they're certainly no substitute for a more thorough treatment.
 

1. What is the difference between calculus and analysis?

Calculus is a branch of mathematics that deals with the study of change and motion, while analysis is a more advanced branch that focuses on the rigorous study of functions, limits, and continuity.

2. Why is it important to study both calculus and analysis?

Studying both calculus and analysis allows for a deeper understanding of the fundamental concepts and techniques in mathematics. This knowledge is essential for advanced studies in fields such as physics, engineering, and economics.

3. Which books are recommended for transitioning from calculus to analysis?

Some popular books for transitioning from calculus to analysis include "Introduction to Analysis" by Arthur Mattuck, "Calculus" by Michael Spivak, and "Analysis I" by Terence Tao.

4. Is self-study possible when learning calculus and analysis?

Yes, self-study is possible when learning calculus and analysis. However, it is recommended to have a strong foundation in calculus before delving into analysis, and seeking guidance from a teacher or tutor can be helpful.

5. How can I apply the concepts learned in calculus and analysis to real-world problems?

The concepts learned in calculus and analysis have practical applications in various fields, such as physics, engineering, and economics. By understanding these concepts, you can analyze and solve real-world problems with more precision and accuracy.

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