It's been a while now since I've picked it up, but I think the main content it assumes your comfortable with is on the order of a semester of Quantum Mechanics. Otherwise, it definitely uses quite a few tricks in calculus (e.g. integrating probability amplitudes, variational calculus, and likely some higher dimensional stuff). The later chapters probably get even more exotic, but the book prepares the reader pretty well I think.
For book recommendations, the ones that come to the top of my mind are:
- Griffiths' Quantum Mechanics [0]. It's become a pretty standard undergrad QM text, and in my experience was very approachable.
- Div, Grad, Curl, and all that by Schehey [1]. I don't remember how much into vector calculus the QFT book got, but this one turned the tide of my undergrad personally. For ~120 pages it gave me a better intuition with 3D calculus than any other resource.
- Something that covers calculus of variations, Euler-Legrange equation, etc. I first covered this in Classical Mechanics but don't remember the textbook. The Feynman Lectures of Physics [2] probably covers it, but I don't know for certain. Incidentally, Feynman is all over QFT, so his undergrad materials are probably excellent prep materials.
I don't remember whether the book introduces bra-kets (Dirac notation) or assumes them, and I don't remember if Griffiths uses it at all. I first saw this notation in General Relativity, with Spacetime and Geometry [3], but I think there are definitely better materials that can explain the notation better.
I'm pretty sure all of these books, and plenty more on these topics, should be widely (or freely) available. Good luck :)
Something that covers calculus of variations, Euler-Legrange equation, etc. I first covered this in Classical Mechanics but don't remember the textbook. The Feynman Lectures of Physics [2] probably covers it, but I don't know for certain.
Caltech is fantastic. They even have the old-form domain name there in your links, similar to Stanford CS department which is also exceptional in the nomenclature, but grandfathered in.
The Feynman lectures have a reputation for being very hit and miss. People who "get it" will find them really interesting and useful. But if you don't, then it might just confuse you.
I know a condensed matter postdoc who told me he felt ready to tackle the Feynman lectures only after he had completed his phd....
They're a great companion book, but you really need a book that guides you through derivations and computations. Some techniques are non-obvious like choosing coordinate systems to make integrals easier, clever contours when applying residue theorem, change of variables using orthogonal matrices to diagonalize symmetric matrices, etc.
For book recommendations, the ones that come to the top of my mind are:
- Griffiths' Quantum Mechanics [0]. It's become a pretty standard undergrad QM text, and in my experience was very approachable.
- Div, Grad, Curl, and all that by Schehey [1]. I don't remember how much into vector calculus the QFT book got, but this one turned the tide of my undergrad personally. For ~120 pages it gave me a better intuition with 3D calculus than any other resource.
- Something that covers calculus of variations, Euler-Legrange equation, etc. I first covered this in Classical Mechanics but don't remember the textbook. The Feynman Lectures of Physics [2] probably covers it, but I don't know for certain. Incidentally, Feynman is all over QFT, so his undergrad materials are probably excellent prep materials.
I don't remember whether the book introduces bra-kets (Dirac notation) or assumes them, and I don't remember if Griffiths uses it at all. I first saw this notation in General Relativity, with Spacetime and Geometry [3], but I think there are definitely better materials that can explain the notation better.
I'm pretty sure all of these books, and plenty more on these topics, should be widely (or freely) available. Good luck :)
[0] https://www.goodreads.com/book/show/153908.Introduction_to_Q...
[1] https://www.goodreads.com/book/show/703104.Div_Grad_Curl_and...
[2] https://www.goodreads.com/book/show/5546.The_Feynman_Lecture...
[3] https://www.goodreads.com/book/show/259680.Spacetime_and_Geo...
Edit: newlines always get me