List of GOOD multivariable calculus book

In summary, some highly recommended books on multivariable calculus that include material on differential forms are Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard and Vector Calculus by Colley. Other similar books that are worth checking out are Fleming's Functions of Several Variables, which also covers measure theory and Lebesgue integration, and Edwards and Marsden's books, although they may be considered too dry. However, Fleming may be particularly helpful for those interested in studying mathematical probability, algebraic topology, mathematical physics, computational geometry and graphics, or analysis. It is also well-structured and pedagogical, with a good balance between Munkres and Spivak's approaches.
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Books on multivariable calculus that I often see get good recommendations are,

Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard
Vector Calculus by Colley

What are other good books with some material on differential forms like Hubbard and Colley?

Books by Edwards, Marsden , etc are just too dry, Hubbard is a better version of Marsden while Colley is fine and includes a short chapter on forms. Are there any books comparable to Hubbard? Hubbard's book is just too long.
 
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Fleming's Functions of Several Variables is good. It technically has the same prerequisites as something like Hubbard & Hubbard or Spivak's Calculus on Manifolds.

However, Fleming has a slightly different overall focus. It covers the same material, but also introduces measure theory and Lebesgue integration. This makes it a good book to recommend as part of a sequence of books on a path to various graduate level disciplines. I'd say that Fleming would be a particularly good recommendation for those who intend to eventually study mathematical probability, algebraic topology, mathematical physics, the mathematical side of computational geometry and graphics, or analysis. I'm surely missing some other disciplines Fleming is good in preparation for.

Also, it's pretty decent pedagogically. It's like a combination of some of the good qualities from Munkres and Spivak. Like most of these books, though, I find it to be light on practical applications and exercises for the generalized Stokes' Theorem. If someone made a book like Fleming with two extra chapters on how and when to apply Stokes' Theorem to proofs or calculations, that would be great.
 
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Related to List of GOOD multivariable calculus book

1. What are the top recommended multivariable calculus books for beginners?

Some of the top recommended multivariable calculus books for beginners include "Calculus: Early Transcendentals" by James Stewart, "Multivariable Calculus" by James Stewart and Daniel Clegg, and "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba. These books are well-written, have clear explanations, and provide a good foundation for further study in multivariable calculus.

2. Are there any multivariable calculus books that focus on real-world applications?

Yes, there are several multivariable calculus books that focus on real-world applications, such as "Calculus: Concepts and Contexts" by James Stewart and "Calculus with Applications" by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. These books use real-life examples and problems to help students understand how multivariable calculus can be applied in various fields, such as engineering, physics, and economics.

3. Which multivariable calculus book is best for self-study?

For self-study, "Calculus: Early Transcendentals" by James Stewart and "Multivariable Calculus" by James Stewart and Daniel Clegg are highly recommended. These books have a comprehensive and easy-to-follow approach, with plenty of practice problems and exercises for self-assessment. They also come with online resources, such as video tutorials and interactive practice quizzes, to aid in self-study.

4. Are there any multivariable calculus books that are suitable for advanced students?

Yes, "Advanced Calculus" by Gerald B. Folland and "Multivariable Mathematics" by Theodore Shifrin and Michael Spivak are two popular choices for advanced students. These books cover more advanced topics in multivariable calculus, such as differential forms, manifolds, and vector bundles, and are often used as textbooks for upper-level undergraduate or graduate courses.

5. What are some important factors to consider when choosing a multivariable calculus book?

When choosing a multivariable calculus book, it is important to consider the level of the book (beginner, intermediate, or advanced), the style and approach of the author, and the availability of online resources and practice materials. It is also helpful to read reviews and seek recommendations from professors or other students who have used the book in their studies.

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