Calculus Looking for a book that teaches mathematics within a physics context

[inthenickoftime]

Sort of like the one by Morris Kline titled "Calculus: An Intuitive and Physical Approach". However this one barely scratches the surface as far as ODE and multivariable calculus go. In short I'm looking for a sequel.

 

[Dr Transport]

https://www.amazon.com/Books-Ivan-Savov/s?rh=n:283155,p_27:Ivan+Savov

 

[mathwonk]

I must be missing something. The linked book(s) seems to go less far, not further, at least mathematically, than the book the OP already read. In particular the BS guide to math and physics seems to end with one variable calc and to have no partial derivatives or several variable integration at all. Was there some more advanced book by this author, or did i miss it in his volume?

 

[inthenickoftime]

I must be missing something. The linked book(s) seems to go less far, not further, at least mathematically, than the book the OP already read. In particular the BS guide to math and physics seems to end with one variable calc and to have no partial derivatives or several variable integration at all. Was there some more advanced book by this author, or did i miss it in his volume?

Exactly. I had a glance at the table of contents and it has less content. What I'm looking for is really a book or resource that teaches multivariable calculus within the context of mechanics/electromagnetism. A sort of marriage so to this speak between physics and math. I liked Morris Kline's recipe of teaching calculus using a physical approach and so I'd like to continue down the same road.

 

[S.G. Janssens]

You might like Vector Calculus by Marsden and Tromba. Other books (co-)authored by Marsden may be interesting for you, too.

 

[mathwonk]

I also like Jerry Marsden's book and taught from it to high school students once. It is quite mathematically rigorous however. The Kline approach, where the subject is lavishly explained intuitively, non rigorously, and at great length, as well as illustrated physically, seems not to be easy to find. A review I read of his book called it something of an out of date book and rather unique, though the reviewer liked it for its intended audience.

I wonder how you like the first three sections or chapters, of volume II of Feynman's lectures on physics? He seems to take the approach of not assuming you know the calculus, and explaining it from his, the physicist's, point of view, pretty much from scratch. Hence it is actually harder to understand for me, a mathematician, since it is not theoretically precise enough for me, but may be easier for you since it is tied more closely to the physics. Perhaps I should say that the reason it is harder to understand for me, may be that he is asking me to understand more, not just the math, but also the physics behind the math. For you that may be a plus. It's only 35 pages but gives you the main theorems of gauss, stokes, and so on.

 

[Mondayman]

You may want to have a look at Div, Grad, Curl, and All That. It teaches vector calculus with an emphasis on E&M.

Also, I have a book called Vector Analysis with Applications to Physics and Geometry, by Schwartz, Green, and Rutledge. It teaches basic vector calculus and has chapters on statics, kinematics, dynamics, differential geometry, harmonic functions, electrostatics, magnetism and electrodynamics, and linear vector functions.

In the preface the said "It is the belief of the authors that vector analysis should be considered as both a mathematical discipline and a language of physics". It is a terrific book, and if you can find it I would highly recommend it if you are just learning vector calculus.

 

[inthenickoftime]

I also like Jerry Marsden's book and taught from it to high school students once. It is quite mathematically rigorous however. The Kline approach, where the subject is lavishly explained intuitively, non rigorously, and at great length, as well as illustrated physically, seems not to be easy to find. A review I read of his book called it something of an out of date book and rather unique, though the reviewer liked it for its intended audience.

I wonder how you like the first three sections or chapters, of volume II of Feynman's lectures on physics? He seems to take the approach of not assuming you know the calculus, and explaining it from his, the physicist's, point of view, pretty much from scratch. Hence it is actually harder to understand for me, a mathematician, since it is not theoretically precise enough for me, but may be easier for you since it is tied more closely to the physics. Perhaps I should say that the reason it is harder to understand for me, may be that he is asking me to understand more, not just the math, but also the physics behind the math. For you that may be a plus. It's only 35 pages but gives you the main theorems of gauss, stokes, and so on.

Which one of the 3 books by Marsden and what parts concern high school studies?

I had a look at Feynman's lecture notes and to me it seems he does assume previous knowledge from the reader. For example, in volume II he begins with: "Also we will want to use the two following equalities from the calculus" (2.7)

If I'm correct he doesn't elaborate on the origins of said equalities. To make sure I didn't miss anything I had a look at the first volume and it seems Feynman introduces partial derivatives out of nowhere (47. Sound. The wave equation). Otherwise this seems like a very decent set of lectures. I just need something else to close the gap mentioned above.

edit: I found a contender. "Second Year Calculus" by David Bressoud.

 

[inthenickoftime]

You may want to have a look at Div, Grad, Curl, and All That. It teaches vector calculus with an emphasis on E&M.

Also, I have a book called Vector Analysis with Applications to Physics and Geometry, by Schwartz, Green, and Rutledge. It teaches basic vector calculus and has chapters on statics, kinematics, dynamics, differential geometry, harmonic functions, electrostatics, magnetism and electrodynamics, and linear vector functions.

In the preface the said "It is the belief of the authors that vector analysis should be considered as both a mathematical discipline and a language of physics". It is a terrific book, and if you can find it I would highly recommend it if you are just learning vector calculus.

I could not find the second title you mentioned. Not anywhere. Can you post its table of contents? :D

 

[mathwonk]

I thought Kline covered some partial derivatives. If so I assumed he covered the equation
df = ∂f/∂x dx + ∂f/∂y dy + ∂f/∂z dz. This is a vector equation that says the change in f equals the vector sum of its changes in the three coordinate directions.

The Marsden book was Vector Calculus, by Marsden and Tromba. I taught the linear algebra and several variable calc in it, including differential forms, to a small honors high school class in Atlanta. One of those students became chair of the math department at Brown. Another one was a phi beta kappa physics major at Harvard and physics PhD at Illinois. Several others majored in math at Duke and other places.

Of course this is not normally high school level material. That was probably the only high school in Georgia offering this course. (Not every high school has a college math professor parent donating his services as teacher. And not every high school wants one.)