The forum discussion centers on the search for advanced mathematics books that integrate physics concepts, particularly focusing on multivariable calculus and ordinary differential equations (ODE). Participants recommend several resources, including "Vector Calculus" by Jerry Marsden and Anthony Tromba, and "Div, Grad, Curl, and All That," which emphasizes vector calculus in the context of electromagnetism. The discussion highlights the challenge of finding texts that maintain an intuitive, physical approach similar to Morris Kline's "Calculus: An Intuitive and Physical Approach." Additionally, "Second Year Calculus" by David Bressoud is mentioned as a potential resource for bridging gaps in understanding.
PREREQUISITESThis discussion is beneficial for students and educators in mathematics and physics, particularly those seeking to deepen their understanding of calculus in a physical context. It is especially relevant for high school teachers and advanced students interested in integrating mathematical rigor with physical applications.
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.mathwonk said: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?
mathwonk said: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 A review I read of his book called it something of an out of date book and rather unique, though the reviewer liked it for its intended audience.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.
I could not find the second title you mentioned. Not anywhere. Can you post its table of contents? :DMondayman said: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.