This is not a substitute for a theorem-and-proof numerical analysis text, and it was never meant to be. The book is most useful in the space between the mathematics on the board and the production routine we eventually call from R. We state the problem, build enough of the method to understand its machinery, implement it plainly, and then make the implementation do some work.
That last step matters. A student who can reproduce the update rule but cannot predict what happens when the starting value moves, the step size changes, or the assumptions fail has learned less than the code suggests. The laboratories make those changes cheap. The teaching notes make them deliberate.