Choose Best Book to Learn Advanced Calculus: Callahan or Fleming?

In summary, the conversation discusses the speaker's knowledge of calculus and their desire to learn advanced calculus. They are considering two books, Calculus by Lang and Calculus by Spivak, with Spivak being at a higher level. They also mention wanting to learn differential forms approach and mention two potential books, Advanced Calculus by Callahan and Functions of Several Variables by Fleming. They express a preference for Fleming due to its shorter length and mention potential advantages of Callahan, such as more recent content and more detailed explanations and diagrams. However, they are concerned about missing important discussions in Callahan. The expert recommends Fleming due to its applied topology and Lebesgue integration on \mathbb{R}^n.
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I have a knowledge of Calculus, Differential Equations, and Linear Algebra, I want to learn advanced calculus, but I'm wondering what book is the best choice, I want to learn it rigorously "enough" but not to the point where someone would call me a mathematician i.e. Calculus by Lang vs Calculus by Spivak, certainly Lang is rigorous but Spivak is at a higher level, though Lang is enough for physicist. I also want to learn it in differential forms approach after, i.e, Advanced Calculus: A Differential Forms Approach by Edwards. I have to choices,

Advanced Calculus by Callahan - longer but has more geometric arguments and diagrams
Functions of Several Variables by Fleming - shorter but harder?

I think Fleming has an advantage because it is shorter, but Callahan is newer and might have some topics that are not in Fleming's book, it also has more explanations and diagrams. Which do you think suits me best? Do you think if I read Fleming instead of Callahan I'll miss some important discussions in Callahan? As of now I'm more into Fleming since it's shorter. I don't have much time to read two books fully, so I just need to choose one and concentrate on that.
 
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Fleming's book isn't especially short. I'd like the sections on differential forms to be a bit more fleshed out, but even there it's more verbose than Spivak's Calculus on Manifolds.

I'd recommend Fleming because of the applied topology and Lebesgue integration on [itex]\mathbb{R}^n[/itex].
 

Related to Choose Best Book to Learn Advanced Calculus: Callahan or Fleming?

1. Which book is more comprehensive for learning advanced calculus: Callahan or Fleming?

Both Callahan and Fleming are highly respected textbooks for advanced calculus. Callahan's book covers a wider range of topics, including multivariable calculus and differential equations, while Fleming's book focuses more on rigorous proofs and theoretical concepts. Depending on your learning goals, one may be more suitable than the other.

2. Is one book easier to understand than the other?

This largely depends on the individual's learning style and background. Callahan's book may be more accessible for those with a strong foundation in calculus, while Fleming's book may be better for those who prefer a more rigorous and abstract approach. It is recommended to preview both books and see which style resonates better with you.

3. Do both books have practice problems and solutions?

Yes, both Callahan and Fleming have numerous practice problems and solutions included in the textbooks. However, Callahan's book may have more comprehensive and varied exercises, while Fleming's book may have more challenging and in-depth problems.

4. Can these books be used as a self-study resource?

Yes, both books can be used for self-study. However, it is recommended to have a strong foundation in calculus before tackling advanced topics. It may also be helpful to seek additional resources and guidance from a teacher or tutor.

5. Which book is more suitable for preparation for higher level math courses?

Both Callahan and Fleming are excellent resources for preparation for higher level math courses, such as real analysis or abstract algebra. However, Fleming's book may be better for developing a strong theoretical understanding, while Callahan's book may be better for building problem-solving skills. It is ultimately up to the individual's learning goals and preferences.

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