Should I read Spivak's Calculus as an undergrad in theoretical physics?

In summary, the individual is considering studying physics with a theoretical physics major but is dissatisfied with the traditional approach of memorizing formulas. They have found enjoyment in reading Spivak, but are concerned about its practical value for their degree. They are debating whether to continue with Spivak or switch to a book with a better balance between rigor and application, such as Apostol's Calculus. The individual believes that while being comfortable with mathematics is important for theoretical physics, it may not necessarily be helpful in learning physics. They also feel that Spivak may be too rigorous for calculus in the context of physics.
  • #1
OscarV
7
1
I am about to start a physics with theoretical physics major, I've taken calculus before but I've not been satisfied with the "memorization of formulas" type books.

I started to read Spivak and found it enjoyable, but since it's a major undertaking I am also concerned for the practical value of reading it to my degree, I am afraid that the book is much too abstract and mathematical, but I am also not sure since as far as I know (which granted, is not much) theoretical physics highly overlaps with pure mathematics.

In a nutshell: Will it actually be useful for my degree (I am confident I want to remain in the theoretical area) or should I read another book that perhaps has a better balance between rigor and application (I've heard Apostol's Calculus to be a good option).

Cheers and thank you in advance!
 
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  • #2
My thoughts are, being able to prove a+b is commutative doesn't necessarily help with learning physics. But the more comfortable you are with mathematics, the better off you will be in the long run, particularly if you plan to do theoretical physics.

But at the end of the day, I think Spivak is slightly overkill for calculus for physics. Perhaps it's my inexperience showing, but nothing I learned during my stint at uni would have been easier had I worked through a rigorous calculus textbook.
 
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Likes dsatkas and Demystifier
  • #3
OscarV said:
I am about to start a physics with theoretical physics major, I've taken calculus before but I've not been satisfied with the "memorization of formulas" type books.

I started to read Spivak and found it enjoyable, but since it's a major undertaking I am also concerned for the practical value of reading it to my degree, I am afraid that the book is much too abstract and mathematical, but I am also not sure since as far as I know (which granted, is not much) theoretical physics highly overlaps with pure mathematics.

In a nutshell: Will it actually be useful for my degree (I am confident I want to remain in the theoretical area) or should I read another book that perhaps has a better balance between rigor and application (I've heard Apostol's Calculus to be a good option).

Cheers and thank you in advance!
I would go for Spivak yes. It doesn't help directly but if you want to be a theoretical physicist it helps to know the rigorous rules of mathematics. The first indirect gain is to be able to think in a more structured and self-critical way. The second indirect gain is that later on learning physics will be much easier when you get to upper undergrad.
 

Related to Should I read Spivak's Calculus as an undergrad in theoretical physics?

1. Should I read Spivak's Calculus as an undergrad in theoretical physics?

It depends on your specific goals and interests. Spivak's Calculus is a rigorous and challenging textbook that covers the fundamentals of calculus in a theoretical and proof-based approach. If you are interested in developing a strong foundation in calculus and have a passion for theoretical physics, then reading Spivak's Calculus could be beneficial for you.

2. Is Spivak's Calculus necessary for understanding theoretical physics?

No, it is not necessary. There are many other textbooks and resources available that cover calculus in a more applied and practical manner, which may be more suitable for understanding theoretical physics. However, reading Spivak's Calculus can provide a deeper understanding and appreciation for the mathematical concepts used in theoretical physics.

3. How difficult is Spivak's Calculus?

Spivak's Calculus is known for being a challenging textbook, even for advanced students. It requires a strong background in algebra and trigonometry, as well as a willingness to engage with abstract and theoretical concepts. However, with dedication and perseverance, it is certainly possible to understand and master the material.

4. Can Spivak's Calculus be used as a self-study resource?

Yes, Spivak's Calculus can be used as a self-study resource. However, it is important to note that it is a dense and rigorous textbook, so it may be beneficial to have a background in calculus or access to additional resources for clarification and practice problems.

5. Are there any alternatives to Spivak's Calculus for learning theoretical physics?

Yes, there are many other textbooks and resources available for learning calculus in the context of theoretical physics. Some popular alternatives include "Calculus: Early Transcendentals" by James Stewart and "Mathematical Methods for Physics and Engineering" by K.F. Riley, M.P. Hobson, and S.J. Bence. It may be helpful to consult with your professor or academic advisor to determine the best resource for your specific needs and goals.

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