Which Calculus book is best for a physics major seeking a challenge?

[Opus_723]

I'm a sophomore Physics major, and I'm looking for a solid Calculus review. I've taken classes on Single and Multivariable Calculus before, but the classes didn't push that hard, and the problems in the book (Hughes-Hallett) are all a breeze. I'm looking for something that I can teach myself with and hone my Calculus skills.

I've considered Spivak, but some people say that the added rigor is not all that useful for physicists. I'm interested in doing proofs, but mostly proofs related to physical phenomenon and the equations that describe them, not proofs of the basic properties of integrals and such. (Actually, I'm very interested in both, but physics is my priority right now. I would love to come back to the other stuff later).

But maybe I'm wrong about Spivak. I haven't looked at it yet. I'm just worried it would be too much of a sidetrack from physics right now. If I'm wrong, I'd be glad to try it. But I do want a book that challenges me. I've only had the basic freshman calculus courses, and I'm starting to realize how little they've prepared me. I can do every problem in my Calculus book in at most a couple minutes, which seems a bit silly. I think it speaks poorly to the exercises rather than highly of my skills.

 

[Dr Transport]

Any mathematical methods in physics book would be helpful.

 

[jasonRF]

I agree with Opus 723: a math methods for physics may be the best place to start. Such a book covers basic linear algebra and differential equations - you didn't mention taking those courses but their content is essential. Math methods books will also cover other topics that are of use (some selection of complex variables, partial differential equations, vector calculus, etc). Emphasis will be approximately what you seem to be looking for. Lots of folks around here like the book by Boas.

There is also a well written free ebook by Prof. Nearing that might fit the bill:
http://www.physics.miami.edu/~nearing/mathmethods/

best of luck,

jason

 

[Opus_723]

Thanks for that link to the ebook, from my first glance through, that looks like exactly what I need.

 

[rezeew]

I can understand your frustration with the lack of rigor and challenge in your previous calculus courses. It is important for a physicist to have a strong foundation in calculus, as it is a fundamental tool for understanding and describing physical phenomena.

I would recommend taking a look at the book "Mathematical Methods in the Physical Sciences" by Mary L. Boas. This book is specifically designed for physics students and covers a wide range of mathematical topics, including calculus, differential equations, and linear algebra, all with an emphasis on applications to physics.

Another option is "Calculus for Scientists and Engineers" by William Briggs and Lyle Cochran. This book also focuses on applying calculus to real-world problems in science and engineering.

Both of these books should provide the challenge and rigor that you are looking for, while also being applicable to your studies in physics. It is important to have a strong understanding of the mathematical concepts and techniques used in physics, and these books can help you achieve that.

I would also encourage you to continue exploring and learning about proofs and their applications in physics. While it may not be your top priority at the moment, having a solid understanding of mathematical proofs can greatly enhance your understanding and problem-solving abilities in physics.

I hope this helps and wish you the best in your studies. Keep pushing yourself and never stop learning!