What factors do distinguish undergrad physics textbooks and grad physics textbooks?

Question

I'm an math student pursuing to Master's degree, and I'm taking physics classes as an auditor. (My campus marks them "applied math" and "applied physics", but I don't think that made much difference.)

Though I wanted to take undergrad physics classes, a professor suggested me to take grad physics classes instead. As a result, I ended up taking grad Classical Mechanics, grad Electromagnetism, and grad Quantum Mechanics at once.

And it turns out my math skill really helps! Classical Mechanics utilizes calculus of variations, and it's not a big deal. Electromagnetism utilizes partial differential equations, and it's not a big deal. Quantum Mechanics utilizes linear algebra on Hilbert spaces, and it's not a big deal.

As they seem "easy" so far, I don't see why they set the textbooks as dedicated for grad classes. The grad textbooks are:

• Classical Mechanics by Goldstein, et al.
• Foundations of Electromagnetic Theory by Reitz, et al.
• Principles of Quantum Mechanics by Shankar

For comparison, the undergrad textbooks are:

• Analytic Mechanics by Fowles & Cassiday
• Introduction to Electrodynamics by Griffiths
• Introduction to Quantum Mechanics by Griffiths

Though I haven't read these undergrad textbooks, they're actually easier, right? Take math textbooks as an analogy. Munkres' Topology is definitely easier than Vick's Homology Theory or Arkowitz's Homotopy Theory.

To prevent an opinion-based question, there is the title question: What factors do distinguish undergrad physics textbooks and grad physics textbooks?

Answer 1

they seem "easy" so far

These textbooks are relatively easy. Reitz is often used at the undergraduate level (whereas Jackson is the canonical graduate book). Shankar is only epsilon more difficult than Griffiths. I'm guessing your institution does not have one of the most rigorous graduate physics programs.

What factors do distinguish undergrad physics textbooks and grad physics textbooks?

While it's difficult to speak in generalities, my impression is that undergraduate physics courses are mostly about applied math, especially vector calculus, ODEs, and simple PDEs. If you are completely comfortable with the calculus, you'll find the physics to be very straightforward: it's mostly just applying definitions (e.g., electric field), equations/laws (e.g., Maxwell's equations) and simple models (e.g., dipole radiation). In contrast, the graduate textbooks tend to consider more interesting physics, allowing the math to get relatively ugly when necessary (while cherry-picking a bit so that there will be closed-form solutions). Graduate courses can also use more advanced math; for example, Jackson introduces Green functions in chapter 1.

Answer 2

Like with any discipline, grad and undergraduate books will usually be written very differently (not always since some can take you through your masters program, as it turns out), but in my field anyways, it boils down to background knowledge. Assumed background knowledge, specifically. Stats books in undergrad are interchangeable, in my opinion. They mostly cover the same material but in different ways. They usually assume students have little exposure to calculus and serious math.

At the graduate level, it's a pretty big jump. Books in undergrad will not assume you've heard of, for example, Rubin's potential outcomes framework. They'll also assume you've never heard of or used formal math proofs. In grad school (phd program mainly), all this is simply background knowledge that the author assumes you know about, so then you can delve into more challenging topics due to the audience being more familiar with the fundamentals. I'm not a math major, but I've seen enough grad textbooks to get what makes them so different, generally speaking.