Spivak v. Anton v. Stewart v. Kline v. Apostol v. Adam. Which is the best?

In summary: So it's definitely a worthwhile read. I'm not sure if it's the best book though.In summary, the two best books for understanding REAL WORLD applications of calculus are Stewart's Differential Equations and Applications, and Howard Anton's Numerical Analysis.
  • #1
potmobius
49
0
Let me further specify: Which of the following texts would be the best for understanding REAL WORLD applications of calculus, and approaching it in a practical manner? Okay, so maybe Spivak and Apostol can be removed from the list as they are a rigorous theoretical approach. How about the rest? Is there a better book than the ones listed? I studied Spivak and understood the theoretical side of Calculus. It was extremely entertaining! I enjoyed it. But I also want to learn the applications of calculus, which Spivak doesn't really go into... I was thinking about Anton or Stewart... any suggestions?
 
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  • #2
Courant also has a lot of applications, but if you already studied Spivak it would be a bit time wasting. I don't know Anton and Stewart. Maybe it's better to just pick up a physics book and do only applications?
 
  • #3
If you've already studied and understood calculus at the level of Spivak, it seems the books you're looking at may be a bit too elementary for you. After all, most of them are introduction calculus books when what you want is calculus applications. A quick amazon search turns up these books, which might interest you:

https://www.amazon.com/dp/0486660974/?tag=pfamazon01-20

https://www.amazon.com/dp/0130111899/?tag=pfamazon01-20

The dover book has the advantage of being very cheap, so even if a lot of it is review for you it's not that much of a loss.
 
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  • #4
Well if you took to time to actually look at some of the problems in any of the books you seemed to have pulled haphazardly into a list, you would realize that the exercises in a text such as Stewart (including the applications) are easily doable if you have seriously studied Spivak (i.e., you did not just read the text, or a few chapters of it).
 
  • #5
My question is very simple. I just want to know which calculus textbook is better, Stewart books or Howard Anton books. I'm not asking about any particular edition but rather a general question about the better explanations of the subject by two different authors.

1) which author's text is most widely used in college/universities? (that is not because you like that book or not)

2) which is the best from these two authors? (from your personal experience) that is nothing to do with either that book is more popular than other.

Please don't suggest any other books, take my question as a comparison between two authors on the same subject.
Thanks
 
  • #6
when you ask a question so narrowly as to preclude our giving you any useful information, you discourage us from responding.
 
  • #7
mathwonk said:
when you ask a question so narrowly as to preclude our giving you any useful information, you discourage us from responding.

Ok sir, I'm extremely sorry. you can give me your suggestions.. i appreciate your concern.
 
  • #8
I must apologize that I won't be answering your question.

If you already know the materials in Spivak, then I would pick any of these books, and read only the chapters that deal with applications. For example, Stewart has a chapter on optimization problems using the theory differentiation, and a chapter that deals with applications of integrals (e.g. in physics, biology, probability, etc). But that's only a small portion of the text. And I imagine that other standard calculus textbooks (e.g. the ones like Stewart) are pretty much the same.

If you want to go further, I also suggest you to study linear algebra and vector calculus as soon as possible. Once you have them down, you should be able to study differential equations, Fourier analysis, numerical analysis, probability, statistics, and well, many subjects that apply calculus that are useful. I think learning those subjects are much more interesting than simply reading the application chapters on Stewart, but it also requires a lot of work.
 
  • #9
One comment, I'll say. Apostol is a favorite for all quantitative scientists (i.e. engineers, economists...). I see it cite all the time when scientist wants to refer to a specific theorem from mathematical analysis.
 

1. What is the main difference between Spivak, Anton, Stewart, Kline, Apostol, and Adam?

The main difference between these individuals is their area of expertise and their contributions to the scientific community. Spivak is known for his work in mathematics, Anton in physics, Stewart in biology, Kline in chemistry, Apostol in engineering, and Adam in computer science.

2. Which of these individuals is considered the best scientist?

It is difficult to say which of these scientists is the "best" as they have all made significant contributions in their respective fields. It is important to recognize and appreciate the unique contributions of each individual.

3. What are some notable achievements of Spivak, Anton, Stewart, Kline, Apostol, and Adam?

Spivak is known for his work in differential geometry and for his influential textbooks. Anton is known for his contributions to quantum mechanics and his development of the Schrödinger equation. Stewart made significant discoveries in genetics and evolution. Kline is known for his work in thermodynamics and statistical mechanics. Apostol is known for his contributions to number theory and mathematical analysis. Adam has made significant contributions to artificial intelligence and computer graphics.

4. How have these scientists impacted the scientific community?

Each of these scientists has made significant contributions to their respective fields, advancing our understanding and knowledge in various areas of science. Their work has inspired and influenced other scientists and has paved the way for further research and discoveries.

5. Are there any controversies surrounding these scientists?

There is no significant controversy surrounding these scientists. However, as with any field of study, there may be differing opinions and debates on certain theories and ideas proposed by these individuals. It is important to approach these debates with an open mind and to continue to critically evaluate and question scientific findings.

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