What's a good book after Kline's Calculus?

In summary, the conversation discusses the best continuation after finishing Kline's Calculus textbook. The options mentioned include Spivak and Apostol Vol. 2, with the caveat that Apostol may be too rigorous for those interested in applied/physics-based Calculus. It is also mentioned that the end volume of Apostol includes an introduction to linear algebra, which is necessary for Apostol Vol. 2. Finally, the suggestion is made to consider Spivak's Calculus and follow-up with his calculus on manifolds.
  • #1
foolsgold229
3
0
Exactly as the title asks, I'm wondering what would be the best continuation to Kline's Calculus textbook. I honestly have found it to be absolutely excellent so far but where would I move to from there? Going to Spivak seems redundant but going to Apostol Vol. 2 seems like it'd be too much of a rigorous leap from the applied/physics-based Calculus that is Kline. Or is it? I'm not really sure... Please advise.
 
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  • #2
What is it that you want to learn from this new book?
 
  • #3
If you are interested in pure mathematics, then I can assure you that Spivak will not be redundant.
 
  • #4
Well, I'm interested in learning multivariate calculus but more so in an introduction to analysis. Though it would seem like Spivak would be the answer. Would it be possible to move from Kline to Apostol Vol. 2 though, for example?
 
  • #5
foolsgold229 said:
Well, I'm interested in learning multivariate calculus but more so in an introduction to analysis. Though it would seem like Spivak would be the answer. Would it be possible to move from Kline to Apostol Vol. 2 though, for example?

For some it is possible, for others not. I would say that for most people it is not possible. But you should probably try yourself.

One other thing, if I'm not mistaken then the end volume of Apostol contains an intro to linear algebra. You will definitely need this for Apostol 2.
 
  • #6
Thank you. I'll certainly consider perhaps going through Apostol Vol. I then. So long as it's not merely a rehash of what I learned from Kline.
 
  • #7
foolsgold229 said:
Thank you. I'll certainly consider perhaps going through Apostol Vol. I then.

Well, that seems redundant. Why not Spivak's Calculus and follow-up with his calculus on manifolds or something?
 

1. What is the best book to read after completing Kline's Calculus?

Some popular options include "Advanced Calculus" by David Widder, "Calculus: A New Horizons Approach" by Howard Anton and Irl Bivens, and "Vector Calculus" by Jerrold Marsden and Anthony Tromba.

2. Are there any books that go beyond Kline's Calculus and cover more advanced topics?

Yes, there are several books that cover more advanced topics such as "Introduction to Calculus and Analysis" by Richard Courant and Fritz John, "A Course in Modern Analysis" by E.T. Whittaker and G.N. Watson, and "Real and Complex Analysis" by Walter Rudin.

3. Is there a book that provides a different approach to learning Calculus compared to Kline's book?

Yes, there are several books that offer a different approach, such as "Calculus" by Michael Spivak, "Calculus: Early Transcendentals" by James Stewart, and "Calculus: One and Several Variables" by Saturnino L. Salas, Einar Hille, and Garret J. Etgen.

4. Can you recommend a book that focuses on real-world applications of Calculus?

"Calculus: Concepts and Contexts" by James Stewart and "Calculus of a Single Variable" by Ron Larson and Bruce Edwards both provide real-world applications and examples of Calculus concepts.

5. Are there any books that can help me review and reinforce the concepts I learned in Kline's Calculus?

Yes, there are many review books available, such as "Calculus: Early Transcendental Functions" by Robert T. Smith and Roland B. Minton, "Schaum's Outline of Calculus" by Frank Ayres Jr. and Elliott Mendelson, and "Cracking the AP Calculus AB Exam" by The Princeton Review.

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