Rigorous book for multivariable + vector calc?

In summary, the conversation discusses recommendations for a book to learn multivariable and vector calculus in a rigorous fashion, with a preference for the treatment of vector calculus to stick to R3. The book "Apostol II" is mentioned as a potential option, but the price and personal preference are concerns. The speaker also mentions not wanting to pay for additional content on linear algebra. They ask for other books that give a linear algebra treatment and specify a preference for classical treatments, rather than modern ones like Spivak Manifolds or Munkres. The expert summarizer recommends John Hubbard's Vector Calculus, Linear Algebra, and Differential Forms as an outstanding choice.
  • #1
khemix
123
1
whats a good book to learn multivariable and vector calculus in a rigorous fashion, similar to spivak. id prefer the vector calculus to stick to R3 (ie stokes), ill save the n case for analysis.

apostol II looks like a good book, but its very expensive and i generally don't like apostol. any other books that give a linear algebra treatment?

and please don't recommend spivak manifolds or munkres. those are modern treatments. I am looking for classical.

(note: i would consider apostol II if i had the table of contents for 1st edition; i don't want to pay extra money for linear algebra which i already know)
 
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  • #2
John Hubbard's Vector Calculus, Linear Algebra, and Differential Forms is outstanding. I recommend it highly.
 

1. What is the best book for learning multivariable and vector calculus?

The answer to this question may vary depending on individual learning styles and preferences. However, some commonly recommended books for rigorous study of multivariable and vector calculus include "Advanced Calculus" by Patrick Fitzpatrick, "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba, and "Multivariable Calculus" by James Stewart.

2. What topics are covered in a rigorous book for multivariable and vector calculus?

A rigorous book for multivariable and vector calculus will typically cover topics such as vector functions, partial derivatives, multiple integrals, line and surface integrals, vector fields, Green's theorem, Stokes' theorem, and the divergence theorem. It may also include topics such as applications of multivariable calculus to physics and engineering problems.

3. How can I effectively study from a rigorous book for multivariable and vector calculus?

It is important to have a strong understanding of single variable calculus before diving into multivariable and vector calculus. Additionally, it is helpful to work through practice problems and proofs to solidify understanding and improve problem-solving skills. Collaborating with peers or seeking help from a tutor or professor can also be beneficial.

4. Is a rigorous book for multivariable and vector calculus suitable for beginners?

No, a rigorous book for multivariable and vector calculus is typically not suitable for beginners. It is designed for students who already have a strong foundation in single variable calculus and are ready for more advanced concepts and rigorous proofs.

5. Are there any online resources that can supplement a rigorous book for multivariable and vector calculus?

Yes, there are many online resources available such as lecture videos, practice problems, and interactive demonstrations that can supplement a rigorous book for multivariable and vector calculus. Some recommended websites include Khan Academy, MIT OpenCourseWare, and Paul's Online Math Notes.

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