Need a good book on the theories of Calculus

In summary, the person is looking for a book that provides more theory on calculus without being expensive. They have already gone through Stewart's Calculus and have been recommended Spivak's book, but cannot afford it at the moment. Another suggestion is Analysis by Tao, which comes in two volumes. The person also mentions looking into Tom Apostol's Calculus volume 1 for rigorous and theory-based content. Finally, they are advised to try finding a used book or downloading a torrent version. Alternatively, they can find many sources for elementary analysis on the internet.
  • #1
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Okay, so I've gone through calc I - III with Stewart's Calculus... I'm happy with the book for the most part, but I want a bit more theory now. I don't care what type of book, it could be like a pop-sci book for all I care, I just want to read about the theories behind the calculus without going broke. I've been recommended Spivak's book already but I can't afford a copy for another couple of weeks and wanted to see if anyone had any cheaper suggestions...Thanks in advance.
 
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  • #2
Have you looked into Analysis by Tao?
 
  • #3
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  • #4
I'm referring to both volumes. Try looking around on other website because the book is hard to find, but well worth it.
 
  • #5
I'll look into it. Thank you for the recommendation.
 
  • #6
I'm going through Tom Apostol's Calculus volume 1 by myself and it's very rigorous and theory based. It really fills in all the mathematical whys behind Stewart's Book.

You can find a used book for cheap or download a torrent of the book (there are many out there).
 
  • #7
Solution: Internet!

There are so much elementary analysis sources on the web that an actual text is unnecessary.

Example: http://www.maths.mq.edu.au/~wchen/ln.html

A google search on "real analysis pdf" should be sufficient
 

1. What is Calculus and why is it important?

Calculus is a branch of mathematics that deals with the study of change and motion. It is important because it provides the fundamental tools and techniques for understanding and solving problems in areas such as physics, engineering, economics, and computer science.

2. Which book is best for learning the theories of Calculus?

There are many great books on Calculus, but some popular recommendations are "Calculus: Early Transcendentals" by James Stewart, "Calculus" by Michael Spivak, and "Calculus: An Intuitive and Physical Approach" by Morris Kline.

3. Is it necessary to have a strong background in mathematics before studying Calculus?

It is recommended to have a solid foundation in algebra, trigonometry, and basic geometry before studying Calculus. However, some introductory Calculus books do cover these topics as well.

4. Are there any online resources for learning the theories of Calculus?

Yes, there are many online resources available for learning Calculus such as video lectures, interactive tutorials, and practice problems. Some popular websites for Calculus include Khan Academy, Coursera, and MIT OpenCourseWare.

5. How can I apply the theories of Calculus in real life?

The concepts of Calculus can be applied in many real-life situations, such as calculating the velocity and acceleration of moving objects, determining the maximum and minimum values of functions, and finding the area under a curve. It is also used in fields such as economics, engineering, and physics to model and solve real-world problems.

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