Where to start physics instruction?

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Due to a myriad of unfortunate circumstances, I'm now schooling myself online. I'm currently a Senior in high school, and I intend to graduate before April. So here I am just finishing up calculus, and having just realized that I can study both multivariable calc/Linear algebra at the same time, I'm left wondering whether or not I'm going down the right path...

From my understanding, the level of mathematics required for Quantum Mechanics/Field theory and General/Special relativity goes up to Partial Differential equations.

So I just want to make sure I'm familiar with the proper mathematics pathway: Calc -> Multivariable/Linear Algebra -> Complex Analysis/Fourier Series -> Differential Equations -> Partial Differential Equations -> Lifelong happiness? (Haha)

And to be completely honest, though I have been teaching myself advanced mathematics, I've yet to find a satisfactory Introduction to physics textbook. As of this moment, I'm currently covering R. Shankar's Open Yale Physics lectures

(Book links: https://www.amazon.com/dp/0300192207/?tag=pfamazon01-20)

(https://www.amazon.com/dp/0300212364/?tag=pfamazon01-20)

However, unlike my mathematics curriculum, which makes it's axioms,proofs, and processes clear, this series seems very ambiguous. When I take the questions provided on the Open Yale course, they seem unrelated to the respective lecture, and when I try and look up alternative sources, they're not comprehensive enough.

My initial plan was to finish calculus before starting any form of physics, thinking it would give me an advantage, however now I'm going ahead with my mathematics instruction, and I've yet to find a decent start in physics.

I intend to take the AP physics tests in May, and provided I can find a decent curriculum, I should be fine. My overall goal isn't to merely pass the exams, but rather to develop a firm understanding of the material.

And regarding the mathematics instruction, I've purchased all the necessary books. If I'm correct, I could very well be set until graduate level maths. Given my study habits allowed me to learn calc within 3 months, My naive estimate is that I could very well understand Diff eqs before september if I'm dedicated enough. However it's difficult to find any comprehensive course outside of university itself for anything outside of mathematics.

So what should I do? Where can I find a comprehensive curriculum? Is my understanding of the maths required correct? If possible, I want to study quantum field theory before I graduate university.
 
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Student100
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Due to a myriad of unfortunate circumstances, I'm now schooling myself online. I'm currently a Senior in high school, and I intend to graduate before April. So here I am just finishing up calculus, and having just realized that I can study both multivariable calc/Linear algebra at the same time, I'm left wondering whether or not I'm going down the right path...

After single variable calculus that is the right course to continue on.

From my understanding, the level of mathematics required for Quantum Mechanics/Field theory and General/Special relativity goes up to Partial Differential equations.

That would not be correct in general.

So I just want to make sure I'm familiar with the proper mathematics pathway: Calc -> Multivariable/Linear Algebra -> Complex Analysis/Fourier Series -> Differential Equations -> Partial Differential Equations -> Lifelong happiness? (Haha)

I would do ODE/PDE before complex, but thats not a hard and fast requirement. You probabaly won't get there before starting university courses in which you should focus most of your energy. [You should also be doing this in high school, but I'm assuming you already are.]

And to be completely honest, though I have been teaching myself advanced mathematics, I've yet to find a satisfactory Introduction to physics textbook. As of this moment, I'm currently covering R. Shankar's Open Yale Physics lectures

(Book links: https://www.amazon.com/dp/0300192207/?tag=pfamazon01-20)

(https://www.amazon.com/dp/0300212364/?tag=pfamazon01-20)

Physics H&R 4th/5th edition volume 1, or K&K introduction to mechanics.

However, unlike my mathematics curriculum, which makes it's axioms,proofs, and processes clear, this series seems very ambiguous. When I take the questions provided on the Open Yale course, they seem unrelated to the respective lecture, and when I try and look up alternative sources, they're not comprehensive enough.

I have no experience with these videos, I would just read the textbook, think, and practice.

My initial plan was to finish calculus before starting any form of physics, thinking it would give me an advantage, however now I'm going ahead with my mathematics instruction, and I've yet to find a decent start in physics.

I intend to take the AP physics tests in May, and provided I can find a decent curriculum, I should be fine. My overall goal isn't to merely pass the exams, but rather to develop a firm understanding of the material.

And regarding the mathematics instruction, I've purchased all the necessary books. If I'm correct, I could very well be set until graduate level maths. Given my study habits allowed me to learn calc within 3 months, My naive estimate is that I could very well understand Diff eqs before september if I'm dedicated enough. However it's difficult to find any comprehensive course outside of university itself for anything outside of mathematics.

So what should I do? Where can I find a comprehensive curriculum? Is my understanding of the maths required correct? If possible, I want to study quantum field theory before I graduate university.

You won't be ready for graduate level math after finishing CA/PDE/ODE whatever. You would need to study things like number theory, anaylisis, group theory, whatever.
 
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