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Good Resources / Best way to self study mathematical methods.

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    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!!
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    (Original post by tangotangopapa2)
    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?
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    (Original post by langlitz)
    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. :unsure: Maybe I should learn vector calculus from the first chapter of Griffiths book. :unsure:

    I have completed my A-levels but never been to university.
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    (Original post by tangotangopapa2)
    Thank you for the reply.
    I would have loved to see more worked examples in RHB. :unsure: Maybe I should learn vector calculus from the first chapter of Griffiths book. :unsure:

    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
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    (Original post by langlitz)
    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.
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    (Original post by tangotangopapa2)
    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
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  1. File Type: pdf Vector Calculus Notes.pdf (804.3 KB, 9 views)
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    (Original post by langlitz)
    Here you go Bear in mind that a lot of the content is explored in more detail in tutorials
    Thanks again I will keep that in my mind
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    (Original post by tangotangopapa2)

    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)?
    Given that you're learning them with an eye to studying physics, I would suggest that you take a look at chapters 2 and 3 (amongst others) of Volume 2 of the Feynman Lectures on Physics:

    http://www.feynmanlectures.caltech.edu/II_toc.html

    2) What is the best way (fastest method) to learn the mathematical methods?
    I guess by "mathematical methods" here, you mean vector calculus?

    In mathematical subjects, "to learn" means "to get to a point where I can solve problems well", rather than "to get to a point where I can waffle convincingly about the subject" (sociology is that-a-way --->). That means that you must find problems, and learn to solve them. Given that you want to learn physics, then I would suggest that you solve vector calculus problems with a physics bias. You can find many in this book, which is both comprehensive and cheap:

    "Schaum's 3,000 Solved Problems in Physics"

    https://www.amazon.co.uk/Schaums-Sol...4311000&sr=8-1

    or "Schaum's Outline of Vector Analysis" for a slightly more mathematical approach.

    https://www.amazon.co.uk/Schaums-Out...311384&sr=8-1"

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

    Much appreciations. !!Thanks in advance!!
    Handy hint: spend as little time as possible looking for "great theory books which will make me understand everything" - you probably won't have time to read them. Instead:

    1) get some working knowledge of the subject that allows you to start problems
    2) start solving problems
    3) return to the "great theory books" when you feel the need to understand more.

    You will understand the theory a lot better when you have solved some actual problems.
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    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

    Griffiths is an absolutely fantastic book on electromagnetism (as is J D Jackson), but both are quite advanced and not exactly preparatory texts.
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    (Original post by mik1a)
    (as is J D Jackson), but both are quite advanced and not exactly preparatory texts.
    Is Jackson the one who derives a whole bunch of stuff from SR right near the start?
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    !!! 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



    (Original post by atsruser)

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

    .
    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.
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    (Original post by atsruser)
    Is Jackson the one who derives a whole bunch of stuff from SR right near the start?
    I can't remember, but it gets tricky pretty quickly. The latter pages are definitely graduate level.
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    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. It will appeal to the inner Russian theoretical physicist in all of us (and gives a very interesting approach to the Russian education system!)
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    Thank you for the reply.

    (Original post by mik1a)
    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
    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.
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    (Original post by tangotangopapa2)
    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.
    A-levels maths should be fine. Physics is used because there are lots of interesting vector fields in physics, such as the electric field. It's used only as far as required to demonstrate the main aspects of vector calculus. It's certainly not meant as an advanced course. I used it in my first year of university.
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    (Original post by tangotangopapa2)
    !!! 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.
    The Schaum 3000 problems in physics is very progressive and very thorough. One of the best problem books I've ever seen. You need a theory book to get you started though, as it is *purely* problems.

    Yes, having the Feynman Lectures available on line is wonderfully convenient.

    I am currently watching Khanacademy videos in 2X playback speed
    Right. I was going to mention Khan but forgot. Personally I don't get on with videos - I can't flick them back and forth easily, and they either go too slow, or too fast. Or the person has a boring voice, or something silly like that.


    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.
    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)

    I will follow your approach and jump straight into problems from Griffith's electrodynamics and Goldstein's mechanics.
    Griffiths I don't know; but Goldstein? From memory, I'd say that you're being "brave".

    For classical mechanics, try to get a copy of "Introduction to Classical Mechanics" by David Morin - very nice problem oriented approach - lots and lots of solved problems, and lots of ones for you to work as well. Also make sure that you can already handle the M1-M5 A level stuff already. Some of the harder stuff there can be reasonably challenging.

    More generally, take a look at 't Hooft's page on self-teaching theoretical physics:

    http://www.staff.science.uu.nl/~gadd...ist/index.html
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    (Original post by mik1a)
    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...
    for strong graduate students!!! Not really introductory stuff, is it?
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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'

    (Original post by tangotangopapa2)
    2) What is the best way (fastest method) to learn the mathematical methods?
    3) Are there any easy to follow books on this?
    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)?

    (Original post by atsruser)
    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)
    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).
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    (Original post by tangotangopapa2)

    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?
    .
    I think you should dispel the thought that you will be studying any actual 'Advanced' physics to any time soon. There's a reason university is 3/4 years. Trying to learn everything as fast as possible is not really going to be any use to you if you don't understand it.
    Also classical mechanics can be really tough, books like Goldstein and Classical Mechanics by Gregory have some truly brutal questions. Good luck haha
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    (Original post by tangotangopapa2)
    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'
    Yes, Baez usually talks a lot of sense.


    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?
    This question is too vague: the answer will depend upon what resources you have at your disposal to allow you to learn. I note that you are a self-teacher, so your main problem will be the lack of professors to turn to, and lectures to attend, to get you started.

    Generally, you need to figure out what is stopping you from learning, say, multivariable calculus e.g.

    - Is there some prerequisite that you need to learn first?
    - Are you procrastinating in opening the books due to fear, as it seems too daunting?
    - Are you not sure where to start?
    - Do you lack the right resources (books, videos, etc)?

    Once you know why you are having trouble, you can start to solve the real problem.

    Note that these days, it is entirely feasible for someone intelligent to learn a huge amount of maths/physics on their own - there are countless internet resources, and fora where you can pose questions. Much of it will come down to the time that you can devote to the subject. You need a lot of time to read and solve problems.

    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)?
    No. You'll need lots of different books. Read as many different books as you can - sometimes it's just nice to go from one to another when you get bored of the first, sometimes one book will be weak on a particular area, but good on others.

    Note that there are many free maths/physics book these days. I can recommend some if you wish.

    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).
    That's quite feasible - Von Neumann got an undergraduate degree in Chemical Engineering at the same time as he did his PhD in mathematics. He didn't attend the chemistry lectures. So you've got it easy in comparison.

    Handy hint: if you want to learn theoretical physics properly, I'd split your time about 70%/30% towards mathematics initially - the mathematics will take longer to learn than the physics, IMHO.

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