Studying How to self-study physics past High School Level?

[TensorCalculus]

Hello! So I'm a teenage physics enthusiast, who wants to take my knowledge past A-level (or in America I believe this would be high school level) physics.
I've studied multiple textbooks like Young and Freedman's University physics, studied maths from books like mathematical methods for physics and engineering.
I solidified all that by doing lots (like, LOTS) of the practice problems and some Olympiad papers.

I don't really know where to go from here.
I've resorted to surfing the internet, and finding free courses and watching YouTube videos that satisfy my interest, or reading popular science, reading high-school textbooks, and just sitting around.
I'm not entirely sure what books to buy - I fear that if I accidentally skip straight to something too advanced I'll not have strong basics. My teacher told me to just read popular science, but I really enjoy looking at the math behind things and I feel that there are few popular science books (that I've read at least) that satisfy my curiosity.
I do really, really love physics, and want to try and study it further - unfortunately, I'm 13 and have quite a long time till I can study physics in University/College.
Does anyone have any resources they would recommend to me (my interest particularly lies around astronomy and electromagnetism) , or any advice to give?

 

[fresh_42]

Here is a series of articles you might want to read:
https://www.physicsforums.com/insights/early-physics-education-in-high-schools/#toggle-id-1
and
https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947
for the mathematical part of your endeavour.

If you want to learn physics seriously then there is no way to avoid mathematics. Physicists use mathematics like a language and you have to learn that part of mathematics like you learn a language.

 

[TensorCalculus]

Wow- these guides are so detailed! Thank you so much, I'm sure these will be helpful

 

[Frabjous]

Calculus is the basic language of physics. Put yourself on a path to learn it.

 

[TensorCalculus]

Yes - my calculus doesn't go much past second order differential equations. How much calculus do you suggest I learn before going into any depth into any physics topics? Is there anything calculus wise that might not necessarily be taught in math textbooks but that is useful in physics specifically?

 

[Frabjous]

Yes - my calculus doesn't go much past second order differential equations. How much calculus do you suggest I learn before going into any depth into any physics topics? Is there anything calculus wise that might not necessarily be taught in math textbooks but that is useful in physics specifically?

I interpret this to mean that you know integral and differential calculus and ordinary differential equations. You need to learn vector calculus. You should be able to handle sophomore physics with what you know now.
Next you learn tensor analysis, linear algebra, partial differential equations and complex analysis. With this you should be able to handle undergraduate physics.

 

[PeroK]

Yes - my calculus doesn't go much past second order differential equations. How much calculus do you suggest I learn before going into any depth into any physics topics? Is there anything calculus wise that might not necessarily be taught in math textbooks but that is useful in physics specifically?

Your mathematics and physics ought to develop in parallel. Learn the mathematics you need for the physics you are learning.

 

[fresh_42]

I would use the search key "<course name> for physicists + pdf", e.g. "vector calculus for physicists + pdf". This pattern has the following reasons. The "+pdf" part usually leads to lecture notes on university servers somewhere on the globe. The English name for the courses ensures that you will find scripts in English (or change them to your native language, in case it isn't English). And the "for physicists" part I think is important so you won't run into mathematics but into how physicists use mathematics instead. These are a bit different. As I said, physicists use math as language. The mathematical treatment of subjects is often less concentrated on frames and more on theoretical aspects that shouldn't interest you in the first place. You need coordinates and frames all over physics, and this part of mathematics works more like a language than, for example, pure logic.

 

[TensorCalculus]

I interpret this to mean that you know integral and differential calculus and ordinary differential equations. You need to learn vector calculus. You should be able to handle sophomore physics with what you know now.
Next you learn tensor analysis, linear algebra, partial differential equations and complex analysis. With this you should be able to handle undergraduate physics.

Yes, that's what I know. Thank you very much for the list of things I should learn in maths - that's something I've been really stuck on recently! Especially considering my bad habit of learning the physics first and the maths later, that's probably where this comes in:

Your mathematics and physics ought to develop in parallel. Learn the mathematics you need for the physics you are learning

^Yeah, I really need to get better at doing this. Thanks for the advice

I would use the search key "<course name> for physicists + pdf", e.g. "vector calculus for physicists + pdf".

Ok! I've just tried it and you're right - this works very well!

And the "for physicists" part I think is important so won't run into mathematics but into how physicists use mathematics instead. These are a bit different. As I said, physicists use math as language. The mathematical treatment of subjects is often less concentrated on frames and more on theoretical aspects that shouldn't interest you in the first place. You need coordinates and frames all over physics, and this part of mathematics works more like a language than, for example, pure logic.

I never thought about that - I mean I've heard thing like "maths is the language of the universe" but never about how maths is applied differently in physics, not as an abstract discipline/pure logic but a language. It's a great insight (and one that will definitely come in useful when learning maths for physics), thank you very much!

 

[Muu9]

Read "advice for introductory physics" by Kevin Zhou

For a textbook, look at Halliday Resnick Krane, 5th edition

https://oyc.yale.edu/physics/phys-200

https://compos.web.ox.ac.uk/

 

[TensorCalculus]

Read "advice for introductory physics" by Kevin Zhou

For a textbook, look at Halliday Resnick Krane, 5th edition

https://oyc.yale.edu/physics/phys-200

https://compos.web.ox.ac.uk/

^These are all actually so good, I haven't taken a look at the books yet but the course is so good, and thank you for showing me COMPOS. It looks like something I'd really want to do when it starts next year (unfortunately, I'm only in year 9 right now - and this year's one has already started )

 

[CrysPhys]

@TensorCalculus . As an alternative to creating your own curriculum, why not just follow an established university physics curriculum? E.g. MIT has an extensive catalog of free online physics courses: https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum.

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required to take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

 

[Muu9]

@TensorCalculus . As an alternative to creating your own curriculum, why not just follow an established unvversity physics curriculum? E.g. MIT has an extensive catalog of free online physics courses: https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum.

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required o take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

In my opinion, the physics 200 and 201 courses from Yale are better than the 8.01 and 8.02 OCW courses.

 

[jtbell]

In the US at least, many physics students learn vector calculus along with intermediate level E&M. Griffiths's widely used E&M textbook starts out with a chapter or two devoted to vector calculus.

 

[TensorCalculus]

@TensorCalculus . As an alternative to creating your own curriculum, why not just follow an established university physics curriculum? E.g. MIT has an extensive catalog of free online physics courses: https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum.

I found that a lot of their courses were incomplete but you're right - some of MIT's courses are really good (especially the less niche ones, such as the ones on classical mechanics). I just sometimes don't know which ones to pick, or I'm hesitant because the lectures are very long considering the amount of information they actually seem to convey. Are there any good courses you'd suggest?

In my opinion, the physics 200 and 201 courses from Yale are better than the 8.01 and 8.02 OCW courses.

I haven't seen them yet - apart from the one you showed me - I'll take a look!

In the US at least, many physics students learn vector calculus along with intermediate level E&M. Griffiths's widely used E&M textbook starts out with a chapter or two devoted to vector calculus.

I live in England - do you think they'll still be accessible? I have got a few English textbooks for math but none of them are hugely popular/ highly reccommended

 

[CrysPhys]

I found that a lot of their courses were incomplete but you're right - some of MIT's courses are really good (especially the less niche ones, such as the ones on classical mechanics). I just sometimes don't know which ones to pick, or I'm hesitant because the lectures are very long considering the amount of information they actually seem to convey. Are there any good courses you'd suggest?

I don't know what you mean by incomplete. Subject matter (e.g., classical mechanics) is typically covered iteratively at increasing levels of difficulty over several courses (e.g., intro, intermediate, advanced, grad). My suggestion above was to follow the sequence that a physics major at MIT would take:

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required to take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

 

[Muu9]

In the US at least, many physics students learn vector calculus along with intermediate level E&M. Griffiths's widely used E&M textbook starts out with a chapter or two devoted to vector calculus.

I'm not sure Griffiths would be appropriate for OP - I would recommend HRK and/or Fundamentals of Physics by Shankar instead, and maybe Purcell for greater depth.

 

[Muu9]

I don't know what you mean by incomplete. Subject matter (e.g., classical mechanics) is typically covered iteratively at increasing levels of difficulty over several courses (e.g., intro, intermediate, advanced, grad). My suggestion above was to follow the sequence that a physics major at MIT would take:

One issue with this is that the courses a physics major would take (8.012, 8.022 etc) often don't include both lectures and assignments, the way the OCW scholar courses do.

 

[Muu9]

I found that a lot of their courses were incomplete but you're right - some of MIT's courses are really good (especially the less niche ones, such as the ones on classical mechanics). I just sometimes don't know which ones to pick, or I'm hesitant because the lectures are very long considering the amount of information they actually seem to convey. Are there any good courses you'd suggest?

I haven't seen them yet - apart from the one you showed me - I'll take a look!

I live in England - do you think they'll still be accessible? I have got a few English textbooks for math but none of them are hugely popular/ highly reccommended

https://www.bookfinder.com/my/preferences/ - set your destination and use it to find cheap used books. You can also get ebooks anywhere (but keep in mind discussing piracy options like shadow libraries is against physicsforums rules)

 

[CrysPhys]

One issue with this is that the courses a physics major would take (8.012, 8.022 etc) often don't include both lectures and assignments, the way the OCW scholar courses do.

Not sure what your point is. For some of the courses, there are different versions (8.01_ for intro classical mechanics, 8.02_ for intro E&M), ...). For someone studying via OCW, rather than on campus, they would still follow the same sequence, using the versions available online. [ETA: Obviously, OCW students would need to skip required labs, which are not available online.]

 

[TensorCalculus]

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required to take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

(sorry, didn't see this before somehow) - I never considered taking a course on math, for some reason - and you're right, the catalog is quite large.

I don't know what you mean by incomplete. Subject matter (e.g., classical mechanics) is typically covered iteratively at increasing levels of difficulty over several courses (e.g., intro, intermediate, advanced, grad)

Some of the courses only have lecture notes that cover half the syllabus, then for the rest it says something like lecture notes not available, or some courses only have question sets which is obviously not very useful if you don't know the material to begin with. Most are quite good though.

https://www.bookfinder.com/my/preferences/ - set your destination and use it to find cheap used books. You can also get ebooks anywhere (but keep in mind discussing piracy options like shadow libraries is against physicsforums rules)

oh wow - yeah. I used to just buy second hand books off ebay but this is actually so good!

Not sure what your point is. For some of the courses, there are different versions (8.01_ for intro classical mechanics, 8.02_ for intro E&M), ...). For someone studying via OCW, rather than on campus, they would still follow the same sequence, using the versions available online. [ETA: Obviously, OCW students would need to skip required labs, which are not available online.]

Do they also have required math courses to take alongside these? Looking at some of the classical mechanics courses, it doesn't seem like they'd be able to cover all the content with just the math they learn pre-uni (so A-level or Equivalent), especially once you get onto things like Lagrangian/Hamiltonian Mechanics, which show up in mechanics 2.

 

[Muu9]

(sorry, didn't see this before somehow) - I never considered taking a course on math, for some reason - and you're right, the catalog is quite large.

Some of the courses only have lecture notes that cover half the syllabus, then for the rest it says something like lecture notes not available, or some courses only have question sets which is obviously not very useful if you don't know the material to begin with. Most are quite good though.

oh wow - yeah. I used to just buy second hand books off ebay but this is actually so good!

Do they also have required math courses to take alongside these? Looking at some of the classical mechanics courses, it doesn't seem like they'd be able to cover all the content with just the math they learn pre-uni (so A-level or Equivalent), especially once you get onto things like Lagrangian/Hamiltonian Mechanics, which show up in mechanics 2.

For the math:
https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/
https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/
For introductory physics, Kevin Zhou recommends Phys 200/201 from Yale over MIT's 8.01SC and 8.02SC: https://knzhou.github.io/writing/Advice.pdf

 

[TensorCalculus]

For the math:
https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/
https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/
For introductory physics, Kevin Zhou recommends Phys 200/201 from Yale over MIT's 8.01SC and 8.02SC: https://knzhou.github.io/writing/Advice.pdf

Yes - this looks really good (and the courses seem to have a lot of resources too which is nice). What's better about the Yale courses in comparison to the MIT ones for physics, do you know? (also - I know I've said this multiple times but thank you all so much for the help - I've been stuck for so long and this has all really helped me)

 

[Muu9]

Yes - this looks really good (and the courses seem to have a lot of resources too which is nice). What's better about the Yale courses in comparison to the MIT ones for physics, do you know? (also - I know I've said this multiple times but thank you all so much for the help - I've been stuck for so long and this has all really helped me)

You can check out both to compare, but I feel the Yale course is more engaging - the OCW mechanics course give Khan Academy vibes. There also no e&m or thermo course with all the features that the OCW mechanics course does.

 

[Homelilly]

Read "advice for introductory physics" by Kevin Zhou

For a textbook, look at Halliday Resnick Krane, 5th edition

https://oyc.yale.edu/physics/phys-200

https://compos.web.ox.ac.uk/

Do you know if the except students from US? I see that only UK students apply, but in the tuition fees, they mention about non-UK students. Thanks for help!

 

[WWGD]

You can check out both to compare, but I feel the Yale course is more engaging - the OCW mechanics course give Khan Academy vibes. There also no e&m or thermo course with all the features that the OCW mechanics course does.

What are " Khan Academy vibes"? I've heard of them but I haven't seen any of their videos.

 

[Muu9]

What are " Khan Academy vibes"? I've heard of them but I haven't seen any of their videos.

Basically they're short clips of a man talking to a screen:

While the Yale courses are full lectures: https://oyc.yale.edu/physics/phys-200/lecture-5

 

[TensorCalculus]

You can check out both to compare, but I feel the Yale course is more engaging - the OCW mechanics course give Khan Academy vibes. There also no e&m or thermo course with all the features that the OCW mechanics course does.

Oh - ok. That makes sense, and I do really need to get a good thermo course (I literally know like ideal gases things (eg. maxwell boltzmann distribution, ideal gas law) and entropy and that's it haha)

Do you know if the except students from US? I see that only UK students apply, but in the tuition fees, they mention about non-UK students. Thanks for help!

yeah I did take a look at the fees because I have friends internationally and was going to tell them about it. They allow international/privately educated students in for a fee of £25 a week (when it is live)

 

[Muu9]

This is a good book on thermodynamics: https://www.amazon.com/Block-Histor...hermodynamics/dp/0198851553?tag=pfamazon01-20
OYC physics 200 also covers thermodynamics

 

[Klystron]

Does anyone have any resources they would recommend to me (my interest particularly lies around astronomy and electromagnetism) , or any advice to give?

Electromagnetism (EM) also has a practical physical side of great value to understanding modern physics. Cognizant of safety rules, if you are able, set up a work area perhaps shared with likeminded serious people, and explore electronic devices and simple projects.

I was thirteen 60 years ago so my examples are dated but you can find modern inexpensive equivalents. I operated a HAM radio transmitter/receiver built with my sister from a kit. We both learned Morse code that came in handy in computer science. I rewired a stereo FM receiver for quadraphonic (4 speaker), added audio from an old B&W television, then designed and built a remote control from a few parts. I helped repair electric appliances and learned how toasters, refrigerators, and TVs operated.

If hands-on physics appeals to you, PF has a a do-it-yourself (DIY) forum with many modern projects. Always underfunded as a teen, consider surplus and second-hand equipment. I imagine local RAF and Royal Navy bases encourage young scientists with workshops, surplus EM gear and old textbooks and manuals. As a teen in Silicon Valley (Santa Clara County, CA) I attended science fairs, open houses and workshops at SRI International and NASA Ames Research Center, later working at both as an adult software engineer. UK contains many research centers.

Astronomy and cosmology teach us so much about the Universe. I shared a basic reflector telescope with my sister, sketching moons while she photographed using a home made adaptor. We also attended shows at our local planetarium and visited Wilson observatory a top Mount Lick. Consider Isaac Newton experimented with Optics while co-inventing Calculus.

 

[TensorCalculus]

This is a good book on thermodynamics: https://www.amazon.com/Block-Histor...hermodynamics/dp/0198851553?tag=pfamazon01-20

Yes - it does look great. Unfortunately I don't have $72.00 to spare (or - well, $40 at least ) so I'll try the course.(the bookfinder you recommended me came in useful)

I was thirteen 60 years ago so my examples are dated but you can find modern inexpensive equivalents. I operated a HAM radio transmitter/receiver built with my sister from a kit. We both learned Morse code that came in handy in computer science. I rewired a stereo FM receiver for quadraphonic (4 speaker), added audio from an old B&W television, then designed and built a remote control from a few parts. I helped repair electric appliances and learned how toasters, refrigerators, and TVs operated.

This sounds so cool - I've been spontaneously inspired to make something when I get home from school

If hands-on physics appeals to you, PF has a a do-it-yourself (DIY) forum with many modern projects. Always underfunded as a teen, consider surplus and second-hand equipment. I imagine local RAF and RN bases encourage young scientists with workshops, surplus EM gear and old textbooks and manuals. As a teen in Silicon Valley (Santa Clara County, CA) I attended science fairs, open houses and workshops at SRI International and NASA Ames Research Center, later working at both as an adult software engineer. UK contains many research centers.

Yes - it does! I haven't seen it yet (newbie here...) but I'll take a look. Luckily for me I live in a very academic city, and both my parents are software engineers so when it comes to DIY with electromagnetism I have a lot of resources. What's RN? (RAF is royal air force... right?)

Astronomy and cosmology teach us so much about the Universe. I shared a basic reflector telescope with my sister, sketching moons while she photographed using a home made adaptor. We also attended shows at our local planetarium and visited a nearby observatory on Mount Lick. Consider Isaac Newton experimented with Optics while co-inventing Calculus.

yes - that's why I am such a big fan. My father is a hobbyist astrophotographer so I have the privilege of owning a telescope - and some of the things I've seen are utterly breathtaking.

 

[Homelilly]

Oh - ok. That makes sense, and I do really need to get a good thermo course (I literally know like ideal gases things (eg. maxwell boltzmann distribution, ideal gas law) and entropy and that's it haha)

yeah I did take a look at the fees because I have friends internationally and was going to tell them about it. They allow international/privately educated students in for a fee of £25 a week (when it is live)

Thanks! It sounds very interesting, I have never heard about it.

 

[TensorCalculus]

Thanks! It sounds very interesting, I have never heard about it.

Yes - me neither (you have Muu9 to thank for the discovery). Oxford uni is (somewhat) in charge of the UK physics Olympiads, so any physics tutoring from them will probably be of quite good quality! What year/grade are you in - do you think you'll do it?

 

[Klystron]

What's RN? (RAF is royal air force... right?)

My bad. I usually write out acronyms on first use. Yes, Royal Air Force and Royal Navy. I once served in a Kingdom where we said Royal Thai Air Force (RTAF) and Royal Thai Navy (RTN) to be polite.

 

[Albertus Magnus]

So glad that you are interested in physics! Those who can do physics should do physics. At any rate the first thing you will study at university will be a freshman physics with calculus type course. We used the popular text by Haliday, Resnick and Walker, this is a classic intro text that has stood the test of time. It provides an intro to mechanics in addition to a brief survey of thermal, electromagnetics, optics and some other topics. Typically this course allows you to get the foundation you need for physics while developing your calculus skills in a calculus I, II & II study.
If you are mathematically competent up through differential equations, then you may well want to try something more advanced like Analytical Mechanics by Fowles and Cassidy or Introduction to Mechanics by Kleppner and Kolenkow; (sophomore/junior level physics) where the last two have been listed in the order of increasing difficulty.
Make sure that you can do all the problems and have mastered the stuff in Haliday and Resnick, further be sure to study mechanics thoroughly before attempting to tackle electromagnetism or quantum mechanics, thermal physics or relativity, as classical mechanics is foundational to the whole of physics and must be mastered at the outset.
If you absolutely must wet your beak with some modern physics consider David Griffith's Revolutions in twentieth Century Physics and David Tong's particle physics course. Finally, when not studying physics commit yourself to studying more and more mathematics: calculus through multivariables and vector analysis, linear algebra, ordinary differential equations, partial differential equations, and complex analysis. Get these topics from a mathematical methods type text such as those from M. Boas, Walker, Arfken, Dennery & Kryswicki or some other good text, however, avoid going off too deep into more purely mathematical texts for a good while as these will tend to take you too far afield in a direction not needed for physics.
Good luck to you in all your academic endeavors!

 

[Mozibur Rahman Ullah]

I'm surprised that nobody has suggested Feynman's Lectures on Physics. There are 3 volumes. They are designed for a university undergraduate curriculum. But a bright teenager should be able to get something out them. Also try out his popular books - it was one of those that inspired me to study physics.

In terms of mathematics, calculus is obviously key as well as linear algebra. You need to become familiar with second order differential equations and how to solve them. From what you've written, it sounds you are familiar with this. Your next step should be learning vector calculus. This is important for classical electromagnetism. This is where you learn about line, surface and volume integrals as well as grad, curl and div and why they're important for and how they're connected to integrals. For more advanced stuff like relativity, learning tensor calculus is important. This branch of mathematics is part of what's called differential geometry.

Its important to realise that mathematicians use mathematics in different ways and motivations than physicists and this difference becomes all the wider as you go deeper into the subject. Differential geometry is a generalisation of vector calculus to curved space and higher dimensions. Both important in general relativity. It also unifies vector analysis in that grad, curl and div are shown to be aspects of a single differential operator - the exterior differential and its also unifies the integral theorems you learn in vector calculus in that they're all shown to be special cases of Stoke's theorem.

Good Luck!

 

[TensorCalculus]

So glad that you are interested in physics! Those who can do physics should do physics

...

At any rate the first thing you will study at university will be a freshman physics with calculus type course. We used the popular text by Haliday, Resnick and Walker, this is a classic intro text that has stood the test of time. It provides an intro to mechanics in addition to a brief survey of thermal, electromagnetics, optics and some other topics. Typically this course allows you to get the foundation you need for physics while developing your calculus skills in a calculus I, II & II study.

Welp - it's quite expensive. It does look like a really useful book though, and if you recommend it so highly to learn the fundamentals of physics, I'll definitely consider it.

If you are mathematically competent up through differential equations, then you may well want to try something more advanced like Analytical Mechanics by Fowles and Cassidy or Introduction to Mechanics by Kleppner and Kolenkow; (sophomore/junior level physics) where the last two have been listed in the order of increasing difficulty.

Make sure that you can do all the problems and have mastered the stuff in Haliday and Resnick, further be sure to study mechanics thoroughly before attempting to tackle electromagnetism or quantum mechanics, thermal physics or relativity, as classical mechanics is foundational to the whole of physics and must be mastered at the outset.

These ones certainly seem more affordable. I am competent up till DEQs I guess, but I might still make sure I know the content from Haliday and Resnick (even if it's just by looking at the covered content online, if I can't manage to convince my parents to lend me like £50) as you said - I don't want to end up skipping something important

If you absolutely must wet your beak with some modern physics consider David Griffith's Revolutions in twentieth Century Physics and David Tong's particle physics course. Finally, when not studying physics commit yourself to studying more and more mathematics: calculus through multivariables and vector analysis, linear algebra, ordinary differential equations, partial differential equations, and complex analysis. Get these topics from a mathematical methods type text such as those from M. Boas, Walker, Arfken, Dennery & Kryswicki or some other good text, however, avoid going off too deep into more purely mathematical texts for a good while as these will tend to take you too far afield in a direction not needed for physics.

Modern Physics absolutely appeals to me - but I guess since I'm a real beginner I might be better off covering all of the classical mechanics and doing the courses people have mentioned to me first. I'll keep the book in mind though! As for mathematics, I'll avoid really pure mathematical texts then. I definitely need to commit myself more to maths, and I'll try finding the texts you've mentioned - thank you!

Good luck to you in all your academic endeavors!

Thank you very much!

 

[TensorCalculus]

I'm surprised that nobody has suggested Feynman's Lectures on Physics. There are 3 volumes. They are designed for a university undergraduate curriculum. But a bright teenager should be able to get something out them. Also try out his popular books - it was one of those that inspired me to study physics.

I've read them, and they're great (well, volume one and 2, I can't seem to get my hands on a copy of 3)! I do also enjoy some of feynman's popular books - he really has a talent for making things seem so simple.

Your next step should be learning vector calculus. This is important for classical electromagnetism. This is where you learn about line, surface and volume integrals as well as grad, curl and div and why they're important for and how they're connected to integrals. For more advanced stuff like relativity, learning tensor calculus is important. This branch of mathematics is part of what's called differential geometry.

My vector calculus is extremely rudimentary, that's true. I've learnt line and surface integrals but I do need to learn volume integrals and things like grad div and curl, not to mention tensor calculus (my username comes from the tensor calculus seen in CS when working with things such as pytorch or tensorflow... my physics tensor calculus skills are nonexistent). Do you have anything you recommend, aside from the resources I've already been referred to?

Its important to realise that mathematicians use mathematics in different ways and motivations than physicists and this difference becomes all the wider as you go deeper into the subject. Differential geometry is a generalisation of vector calculus to curved space and higher dimensions. Both important in general relativity. It also unifies vector analysis in that grad, curl and div are shown to be aspects of a single differential operator - the exterior differential and its also unifies the integral theorems you learn in vector calculus in that they're all shown to be special cases of Stoke's theorem.

Yes - this has come to my attention the past few days with what everyone has been telling me! I am yet to learn much differential geometry at all, but from what I've learnt online it sounds really interesting and something I might have looked into just for the fun of the maths, even if it weren't important for physics.

Good Luck!

Thank you!!

 

[Muu9]

I found this interesting comment:
I have heard good things about Visual Differential Geometry and Forms by Tristan Needham, but it's about 32 pounds used on bookfinder.
Are there any university libraries you could enter, even if you can't borrow the books inside?

 

[Muu9]

One additional option: consider explaining your situation to your school librarian or a local public librarian. They might be able to request a copy from another library (Inter Library Loan) or know of local university libraries that are open to the public and have the book(s) you need

 

[TensorCalculus]

I have heard good things about Visual Differential Geometry and Forms by Tristan Needham, but it's about 32 pounds used on bookfinder.

That price might actually be doable - I have like £35 worth of random saved cash...

Are there any university libraries you could enter, even if you can't borrow the books inside?

I think Cambridge University and Trinity College have libraries open to the public, but I don't live near enough to go on my own and my parents can't exactly drop me often...

consider explaining your situation to your school librarian or a local public librarian. They might be able to request a copy from another library (Inter Library Loan) or know of local university libraries that are open to the public and have the book(s) you need

This is actually a very feasible option. I'm currently on a scholarship at a really nice private school (COMPOS said that if in a private school on bursary/scholarship they might consider providing it for free thank the lords), that's quite academic and probably has the kinds of links that can get me the books I want. (shocking that I didn't think of it beforehand - thank you for the idea!)
Also I can't see the comment. Probably some kind of network problems.

 

[fresh_42]

That price might actually be doable - I have like £35 worth of random saved cash...

Don't forget that the internet nowadays provides dozens of good lecture notes for free. As long as you aren't focused on a certain lecturer, you can find excellent (and English) sources on many university servers in the world.

 

[TensorCalculus]

Don't forget that the internet nowadays provides dozens of good lecture notes for free. As long as you aren't focused on a certain lecturer, you can find excellent (and English) sources on many university servers in the world.

True, I really should utilize lecture notes more. I tend to just skim read them after watching the lecture and never come back...........

 

[fresh_42]

True, I really should utilize lecture notes more. I tend to just skim read them after watching the lecture and never come back...........

It is one of the things I like about science. It doesn't care where it is written.

 

[Mozibur Rahman Ullah]

I've read them, and they're great (well, volume one and 2, I can't seem to get my hands on a copy of 3)! I do also enjoy some of feynman's popular books - he really has a talent for making things seem so simple.

My vector calculus is extremely rudimentary, that's true. I've learnt line and surface integrals but I do need to learn volume integrals and things like grad div and curl, not to mention tensor calculus (my username comes from the tensor calculus seen in CS when working with things such as pytorch or tensorflow... my physics tensor calculus skills are nonexistent). Do you have anything you recommend, aside from the resources I've already been referred to?

Yes - this has come to my attention the past few days with what everyone has been telling me! I am yet to learn much differential geometry at all, but from what I've learnt online it sounds really interesting and something I might have looked into just for the fun of the maths, even if it weren't important for physics.

Thank you!!

It's probably worth pointing out - if it isn't obvious to you - that the calculus of differential forms that you will come across in any differential geometry course is basically tensor calculus. Given your handle, I thought it important to point this out ;-). The course that I like is John Lee's 3 volume set on manifolds covering topological, smooth and Riemannian manifolds. However it's aimed at mathematicians, so it may not be appropriate you. Another book which is lovely and an easy read and which also covers differential geometry is Baez & Muniain's Gauge Fields, Knots & Gravity. Although they cover advanced material they do it in such a breezy style that its a delight to read.

I've read them, and they're great (well, volume one and 2, I can't seem to get my hands on a copy of 3)! I do also enjoy some of feynman's popular books - he really has a talent for making things seem so simple.

My vector calculus is extremely rudimentary, that's true. I've learnt line and surface integrals but I do need to learn volume integrals and things like grad div and curl, not to mention tensor calculus (my username comes from the tensor calculus seen in CS when working with things such as pytorch or tensorflow... my physics tensor calculus skills are nonexistent). Do you have anything you recommend, aside from the resources I've already been referred to?

Yes - this has come to my attention the past few days with what everyone has been telling me! I am yet to learn much differential geometry at all, but from what I've learnt online it sounds really interesting and something I might have looked into just for the fun of the maths, even if it weren't important for physics.

Thank you!!

It's worth pointing out that the calculus of differential forms that you will come across in any course on differential geometry is basically tensor calculus. I thought it important to point this out given your handle ;-). A lovely book that covers this is Baez & Muniain's Gauge Fields, Knots and Gravity. They cover advanced topics but they do it in such a breezy style that its a delight to read. They don't however cover all the technical details. One set of books that does is John Lee's 3 volume course on topological, smooth and Riemannian manifolds. However, they're aimed at mathematicians. He is however, a very clear writer.

 

[TensorCalculus]

It is one of the things I like about science. It doesn't care where it is written.

This is going on my "favourite quotes of all time" list

It's probably worth pointing out - if it isn't obvious to you - that the calculus of differential forms that you will come across in any differential geometry course is basically tensor calculus. Given your handle, I thought it important to point this out ;-).

What - really? I mean I guess they're doing similar things, but surely they're at least somewhat different? I see people operating on entire tensors at once (like I do when I do coding sometimes, except the computer's doing all the hard work for me in that case) - is that actually the same thing as integrating over a vector field (such as when looking at line integrals, surface integrals etc in things such as Gauss's law and Ampere's law?)

The course that I like is John Lee's 3 volume set on manifolds covering topological, smooth and Riemannian manifolds. However it's aimed at mathematicians, so it may not be appropriate you. Another book which is lovely and an easy read and which also covers differential geometry is Baez & Muniain's Gauge Fields, Knots & Gravity. Although they cover advanced material they do it in such a breezy style that its a delight to read.

Sounds good! I might take a look even if it's aimed at mathematicians, Physics may be my passion (and I do therefore steer away from abstract maths) but I am a huge maths nerd too and do enjoy maths just for the fun of it :D

 

[Albertus Magnus]

...

Welp - it's quite expensive. It does look like a really useful book though, and if you recommend it so highly to learn the fundamentals of physics, I'll definitely consider it.


These ones certainly seem more affordable. I am competent up till DEQs I guess, but I might still make sure I know the content from Haliday and Resnick (even if it's just by looking at the covered content online, if I can't manage to convince my parents to lend me like £50) as you said - I don't want to end up skipping something important

I haven't checked on these specific titles, but I often buy physics texts at thrift books or on Ebay, for example I just got an older edition but still perfectly useful copy of Gradshteyn and Rhyzik $20.00 on ebay, whereas a new copy would have cost me about $200.00. A copy of Haliday and Resnick from the 1970s would be just about as good as a more updated copy, and I bet it would be quite affordable. Foundational type subjects like classical mechanics don't change too fast, however, subjects like astronomy on the other hand have developed so much in the last 20 years that it pays to buy newer texts.

 

[Albertus Magnus]

I just wanted to add: the Feynmann Lectures on Physics are available free online and they are awesome! He covers classical mechanics, electromagnetism and quantum While teaching some maths along the way. This would be a good place to get some of that vector calculus.

 

[jtbell]

it's [Halliday/Resnick/Walker] quite expensive.

For self study, there's no need to buy the current edition. Used copies a few editions back, whatever you can find cheaply, are fine for that purpose.

In the US at least, instructors usually assign homework exercises out of the textbook, and often assign specific pages or sections for reading. Publishers change up the book's layout, exercises, etc. in new editions, in order to discourage students from buying used books from others who have already taken the course. At the introductory level, many students are not physics majors, will not be studying physics further, see no reason to keep the book as a reference, and therefore happy to sell their copies if they can.

 

[Muu9]

Halliday Resnick Walker is roughly at the same level as University Physics by Young and Freedman, so I wouldn't bother with the former for someone who has completed the latter.

Here's another idea: ask university libraries in driving distance when they will update their copies of physics/math texts, which usually involves throwing out the old editions, so you can pick them up for dirt cheap or free.