I have studied multivariable calculus of course, along with some basic calculus of vector fields, and I am reviewing some ODEs too (I am forgetting the theory, for some reason, I don't like the idea that I am forgetting what little I know about math theory).
Well, coincidentally, I am reviewing...
^ I can understand these, at least mechanically, but well, I guess, what I am desperately trying to find is a general method that applies to all cases; something in which the usual basic methods is actually a special case of it. What you outlined above is intuitive, but it doesn't seem to fit...
Oh this, I did some searching. Apparently, what I said above about straight forward integrating over the surface S isn't exactly correct. You parametrize the surface (to vector valued function), I think, usually using spherical/cylindrical coordinates then transform it to rectangular components...
Yes, exactly. But the problem here is, he didn't actually tell that the surface integral is a double integral (at least from what I currently know) that can be solved by actually integrating over the surface. In the textbook, after constructing something that's starting to look like a Riemann...
I am saying all those given that my textbook only offers an introduction to calculus of vector fields, so I know asking for a more general approach is a bit unreasonable.
Anyway here's an example of one:
For a function of three variables G(x,y,z), the surface integral of G over the surface S...
I have been restudying vector calculus, especially on topics pertaining to line integrals, surface integrals (and the accompanying vector forms). One problem I have encountered from the book I have been using is that it seems there are some theorems and results that are only restricted to...
@WannabeNewton: There's this math methods for physicists course that I'm required to take, I might put off the more 'mathematically rigorous' texts for now.
@Meir Achuz: I'd try to look for it; I'm finding it weird that the first edition was better than the latest, were the topics discussed...
I might be forced to use the Arfken and Weber text, what might be the best supplement book with it? I've read a lot of bad reviews for it.
I'm thinking of using Boas' but vector analysis starts at the latter part of the book and makes references from the earlier chapters, I might not be able...
I found one, it's: Introduction to Mathematical Reasoning by Peter Eccles. Sorry, I think the thread can be closed now; or not, if you guys think you can still dump more useful books here.
I'm kind of new to proof based mathematics, can you guys give me an advice on what a good book pertaining to this should I get?
I don't really care about what particular subject in mathematics it is, just as long as it can give me a good knowledge and skills in proving, and it's something...
That one by Hassani seems good, I again, found myself progressing quite slowly, but it was nevertheless satisfying so far. I wish it could be a good stepping stone for me to get used to more rigorous mathematics. I might stick with this one.
@MathematicalPhysicist: Classical texts seems...
The book I referenced was by Jeffreys & Jeffreys' Methods of Mathematical Physics. The book seems good, but I think it's more of a supplemental text than a main one that I could use for a course. I found myself progressing really slow; though the book was very interesting.
@rhombusjr: I've...
I found myself having a hard time choosing what mathematical physics text should I stick with. I'd like to think of myself as mathematically inclined, and I would really prefer a mathematical physics book that emphasizes 'the maths' and the proofs and not just the methods while maintaining its...
This is not the first time that I encountered Calculus, I'm quite familiar with the techniques and the big picture but I think I'd like something that has good proofs, I seem to absorb the maths better with nice proofs. Of course, something with good problems too.
I guess I'll be checking out...
I'm just not very familiar with online buying. Also, it's much convenient to buy books within my area.
About your question I'd probably prefer something more rigorous between the two, but if the rigor comes with too much complexity where It's probably something useless for a beginner then I'd...
I'm not sure if this should go here, anyway I'm contemplating over what Calculus text book should I buy. Textbooks that are sold locally are somewhat limited to our country so I only have 2 'good' books to choose from. It's either Leithold's or Stewart's, I don't know which one of these are...