Good Resources / Best way to self study mathematical methods.

I wish to self-study Physics but my maths knowledge is not beyond A levels further mathematics.

In order to strengthen my maths, I am currently following "Mathematical Methods for Physics and Engineering" by K.F. Riley and others. Despite the popularity of the book, I am finding it hard to follow. For instance, the introduction of inner products in the complex field not well presented and made me look for some other resources. There is only 2 and a half page discussion for space curves and lacks enough examples.

My recent goal is to prepare myself for the lecture notes on Classical Dynamics ( http://www.damtp.cam.ac.uk/user/tong/dynamics.html ) and Electromagnetism ( http://www.damtp.cam.ac.uk/user/tong/em.html ) by David Tong.

1) What are some good resources to study mathematical methods (at the moment I am looking for one on vector calculus: gradient, divergence, curl; line, surface and volume integrals; divergence and strokes theorem)?

2) What is the best way (fastest method) to learn the mathematical methods?

3) Are there any easy to follow books on this?

Much appreciations. !!Thanks in advance!!

I found RHB to be pretty good for vector calculus tbh. Introduction to electrodynamics by Griffiths is a great book for electromagnetism

It depends depends what level you are though... Are you undergrad physics? Or just doing A-level?

Thank you for the reply.
I would have loved to see more worked examples in RHB. Maybe I should learn vector calculus from the first chapter of Griffiths book.

I have completed my A-levels but never been to university.

Ok fair enough, I was using RHB as a reference rather than learnings directly from it as I had excellent lecture notes and lots of tutorial questions. The vec calc in the intro of Griffiths is more of a review for people who've studied it in the past I think

I could send you some notes for vec calc if you're interested

Thank you sooooo muchhhhh!!!!!!!! That would be tremendous help.

Here you go Bear in mind that a lot of the content is explored in more detail in tutorials

1) What are some good resources to study mathematical methods (at the moment I am looking for one on vector calculus: gradient, divergence, curl; line, surface and volume integrals; divergence and strokes theorem)?

2) What is the best way (fastest method) to learn the mathematical methods?

3) Are there any easy to follow books on this?

Much appreciations. !!Thanks in advance!!

(as is J D Jackson), but both are quite advanced and not exactly preparatory texts.

I guess by "mathematical methods" here, you mean vector calculus?

.

Is Jackson the one who derives a whole bunch of stuff from SR right near the start?

Surprised nobody's mentioned it yet.

'Div, Grad, Curl and all that' by H M Schey is a fantastic informal intro text to vector calculus

Thank you for the reply.



Looks interesting, I thought it was advanced material seeing all those Qs, epsilons and electric fields at the beginning. I am assuming that one needs at least the knowledge of multiple integrals as a prerequisite.

!!! Many thanks !!!! Really helpful !!!

Never knew that such an easy to read version of Feynman Lectures exists. I was looking for the problems that let me practice in a progressive manner, so I hope Schaum's problem will allow me to do this.

I am currently watching Khanacademy videos in 2X playback speed

By "mathematical methods" I mean mathematical methods for physics (vector calculus to start with but not limited to it).
Since my current goal is to study Classical Mechanics and Electromagnetism for next couple of months, I believe I should be fine with vector calculus and calculus of variations (I am comfortable with simple ODEs). I will again have to learn more mathematical methods before I begin thermodynamics and quantum mechanics.

I will follow your approach and jump straight into problems from Griffith's electrodynamics and Goldstein's mechanics.

I should also add, one to bear in mind, Landau & Lifshitz course on theoretical physics is another fantastic resource, and the first volume is a great handbook for mechanics...

2) What is the best way (fastest method) to learn the mathematical methods?
3) Are there any easy to follow books on this?

OK. But that's a big topic, so you'll need to plan it a bit, or explain your needs here more, to get better answers. You'll certainly need to learn a certain amount of linear algebra and analysis for QM, but you'll also need DEs, and their methods of solution, once you get on to stuff like the Schroedinger eqn for hydrogen.

Thermo is mainly calculus (+of variations)

2) (General Question) Say you really want to study some advanced topic in Physics and it is the maths that puts you off. (For example, Multivariable calculus is putting me off from studying advanced electromagnetism.) In that case, what would be the best (and the fastest) way to overcome the problem?
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Thanks a lot ! ! !
That page on self-teaching theoretical physics looks appealing to me.
I also found this page: http://math.ucr.edu/home/baez/books.html on 'How to learn Maths and Physics'

2) (General Question) Say you really want to study some advanced topic in Physics and it is the maths that puts you off. (For example, Multivariable calculus is putting me off from studying advanced electromagnetism.) In that case, what would be the best (and the fastest) way to overcome the problem?

3) Most of the books named 'Mathematical Methods for Physics/ Physics and Engineering/ Physical Sciences' merely provide themselves as reference books. Is there any such book that one could solely rely on (use it {possibly only it} for self-study)?

I wish to become a theoretical physicist but unfortunately, I will not be attending University soon (that's a different story). So, I am trying to learn as much of physics as I can (on my own).