Vector calculus book recommendation

In summary, the conversation discusses the need for a Vector Calculus book for a physics major planning on pursuing a Master's degree. The individual has been away from math and physics for some time and is looking for a book with rigorous proofs and examples. Suggestions for books such as "Advanced Calculus" by Folland, "Vector Calculus" by Marsden & Tromba, and "Mathematical Methods in the Physical Sciences" by Boas are given. The conversation also mentions the usefulness of taking an easier book such as "Multivariable Calculus" by Stewart to supplement the more advanced texts. The conversation also mentions other classic books in the field.
  • #1
phyz76
2
0
hey guys & gals ...
i need your advice in selecting the best possible Vector Calculus book for a physics major planning on pursuing his Master's and perhaps more in the future ... i have been away from math and physics for some time (~ 4 years) and do not have a solid Vec-Calc background. I've read mixed reviews about different books on amazon.com and can't quite decide on which book to go with. I have a general Calc book from the late 90s but it's not enough for advanced physics (well, as advanced as a master's degree would require).

Your advice is appreciated,

phyz76
8 )
 
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  • #3


Davers,
thanks for your reply. But isn't your recommended book an informal text on vector calculus? it does have great reviews, but i need something more fundamental with rigorous proofs, examples, and problems ... Griffiths which is the typical E&M undergrad also has vector calculus but there isn't much proof and examples. if you have other recommendations like which to choose between "Tromba, Hubbard, Colley, or Stewart" (or another author) as a more formal text on V-Calc, please let me know.
 
  • #5
phyz76 said:
Davers,
thanks for your reply. But isn't your recommended book an informal text on vector calculus?

I've seen the book used as a supplemental text at UCSD for their E&M course.
 
  • #6
Schaum's omits a lot of rigour and/or leaves it as exercise without answers.

The book my school uses is "Advanced Calculus by Folland, and it may be what your looking for. Very rigorous, but at the same time difficult. Its what physicists here are expected to know. Reviews aren't looking too great though. Check it out:
https://www.amazon.com/dp/0130652652/?tag=pfamazon01-20

Another one my school used to use is Vector Calculus by Marsden & Tromba. It too is very rigorous and somewhat theoretical. Check it out:
https://www.amazon.com/dp/0716724324/?tag=pfamazon01-20

These are very difficult texts from what I know, that really go in depth into vector calc. I haven't actually used them yet, because I start my course in a week. However, if your doing independent study, it might be difficult to grasp advanced concepts alone. So I'd recommend you take an easier book to supplement it, something like Stewart's Multivariable calculus which is rich on illustrations and gives you a strong intutitive feel. Once that is down, you can get down to the proofs and rigour in the books I mentioned above.

Hope this helps.
 
  • #7
Here's two that have served me well:

Mathematical Methods in the Physical Sciences by Mary L Boas, Wiley $ Sons
(This one is not at a high level, but thorough)
and
Mathematical Methods for Physicists by Arfken and Weber, Elsevier Academic Press.
(This one seems to come in several versions... The two I have are both useful.)
 
  • #8
i liked tromba and marsden when i taught out of it to hionors high school students about 25 years ago.

the classic for years was williamson, crowell, and trotter. of course apostol.
 
  • #9
mathwonk said:
i liked tromba and marsden when i taught out of it to hionors high school students about 25 years ago.

the classic for years was williamson, crowell, and trotter. of course apostol.

Highschoolers learning from Tromba?

Why do I suddenly feel so much stupider... :(
 
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Likes Joker93

1. What is the best vector calculus book for beginners?

For beginners, a highly recommended vector calculus book is "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by John H. Hubbard and Barbara Burke Hubbard. It provides a comprehensive introduction to the subject with clear explanations and examples.

2. Which vector calculus book is suitable for self-study?

"Vector Calculus" by Jerrold E. Marsden and Anthony Tromba is a great book for self-study. It has a user-friendly layout, numerous exercises and solutions, and covers a wide range of topics in vector calculus.

3. Is there a vector calculus book that focuses on applications?

Yes, "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by John H. Hubbard and Barbara Burke Hubbard has a strong emphasis on applications in physics and engineering. It also includes a chapter on computer graphics.

4. Can you recommend a vector calculus book with a rigorous approach?

"Calculus on Manifolds" by Michael Spivak is a highly regarded book for its rigorous approach to vector calculus. It is a challenging read, but it provides a solid foundation in the subject.

5. What is a good vector calculus book for advanced students?

For advanced students, "A Course in Multivariable Calculus and Analysis" by Sudhir R. Ghorpade and Balmohan V. Limaye is a comprehensive and rigorous book that covers advanced topics in vector calculus and multivariable analysis.

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