This is why graduate-level texts frustrate me. The authors always assume that half the stuff they're discussing in their textbook is obvious to the reader/student who has maybe seen the material once before in an undergraduate course. While some of this material should be expected to be known already, you can't just chuck stuff at your reader and say "it is now obvious that" or "the proof is trivial" when neither of these statements is actually true. If you use either of these statements in your textbook, you're not a good teacher. Period.
The title of this entry comes from the fact that I'm comparing two Electromagnetic Theory textbooks, one by D.J. Griffiths and the other by J.D. Jackson. Griffiths' Introduction to Electrodynamics is a witty, conversational, and informative text that helps undergraduates cope with the fact the E&M is really hard and that most of the concepts are foreign to someone who has only ever dealt with classical mechanics. Jackson's Classical Electrodynamics, on the other hand, is a text where the reader can tell that the author really knows his stuff when it comes to E&M, but has no sense of how to convey that knowledge to someone who is not an advanced student of the subject.
For instance, let's say I were teaching the concept of projectile motion to someone who has never delved into the subject. If I were Griffiths, I would say something like, "All objects in free fall on Earth experience a force due to gravity toward the ground. This force causes all objects to accelerate at the same rate, meaning that the rate at which something speeds up/slows down in Earth's gravity is the same for all objects regardless of how heavy they are. Because this acceleration is constant near the ground, objects tend to follow a parabolic trajectory (if we ignore air resistance). The equations that show this follow from Newton's second law, F = m a. If you don't believe this, let's try it, shall we?"
Now wasn't that nice? This explanation is certainly very clear about what projectile motion is and what causes it. Griffiths enjoys taking concepts that may be hard to comprehend and then following through with some equations/proofs to try and clarify the situation, usually speaking to the reader as though he were sitting down with them helping them through a problem.
What about Jackson? He would probably say something along the lines of, "The reason projectiles follow parabolic paths is simple: if you solve the Hamilton-Jacobi equation in a uniform gravitational field, you will find that the path that minimizes the action is that of a parabola. This can be seen by setting the variation of the Lagrangian equal to zero."
Well that was simple, wasn't it? While technically correct, you probably have no idea what the Hamilton-Jacobi equation or Lagrangian are, nor do you probably know what "action" means in physics. Now you may be thinking, "well, these things are part of undergraduate courses, right?" Well, no, actually. I had no idea what the Hamilton-Jacobi equation was until I took graduate level quantum mechanics, and I was expected to have known that from my graduate classical mechanics course (which I didn't take until my second semester of quantum mechanics). Suffice it to say, there was a lot I had to learn on the fly, but you can probably see what I'm getting at. The assumption that students know everything you expect them to know and have it ready to go the minute you throw that curve ball at them is a terrible way to go about teaching and, in my opinion, does not foster good education.
On an unrelated note, I have a problem set out of Jackson due tomorrow which I haven't finished yet. So, how was your day?