Overview. The listed prerequisites for my Pomona College course are vector calculus, linear algebra, and our sophomore-level intermediate mechanics course (at the level of John Taylor's Classical Mechanics). Our students also have an extensive introduction to special relativity (at the level of Six Ideas That Shaped Physics, Unit R). This book is addressed to students with roughly this level of preparation. However, there is some flexibility with these prerequisites, as I will outline below.
Math Requirements. The minimal math prerequisite is vector calculus. Linear algebra is desirable but not really necessary if students know how to multiply matrices and calculate a matrix inverse. Students familiar will differential equations will be be more comfortable with some of the math in this textbook, but I do not assume this background. Math beyond vector calculus is really desirable only because it gives students greater experience with the process of learning new formalisms and generally working with challenging mathematics.
Intermediate Mechanics or Electrodynamics. The primary point of requiring intermediate mechanics is that it gives students experience in applying some serious (post-calculus II) mathematics to physics problems. The purpose might be equally (or even better) served by requiring electrodynamics at the level of Purcell or Griffiths or any other course that applies vector calculus to physics problems. Students do, however, need to be able to recognize the simple harmonic oscillator equation and its solution, and it would help them to be familiar with the calculus of variations and the differential forms of Maxwell's equations.
Having said this, I have occasionally allowed sophomores who have not taken intermediate mechanics (but who have taken mathematics beyond vector calculus) into the course. My experience is that they have to work very hard and do not generally receive as high a grade for all their work as they would hope, but students with a strong math background can survive the course even without intermediate mechanics (or the equivalent).
Special Relativity. This text does not really provide a comprehensive introduction to special relativity. If students do not have a strong background in special relativity, they will not find chapter 2 to be "a review," and will need to spend more time on this subject. Depending on how much they have seen and what you (the instructor) want to do with this course, you can either spend more than one class session working on chapter 2 (perhaps with the help of some supplemental instructor-supplied materials) or (in the worst case), spend up to two weeks going through a book like Unit R of Six Ideas That Shaped Physics or Taylor and Wheeler's Spacetime Physics. All of the ideas students need to know for this course are provided in chapter 2, but being comfortable with Lorentz transformations, invariant and frame-dependent quantities, spacetime diagrams, proper time, and particularly applying these concepts to real physical contexts would be valuable preparation for the kind of thinking required in the rest of the course.
Spending extra time on special relativity will mean dropping something else later, but instructors do have some flexibility to do so, particularly with the last three sections of the book.
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Thomas A. Moore has been a professor in the Physics and Astronomy Department at Pomona College since 1987. He does theoretical research on detecting gravitational waves using LISA (now eLISA). Send him a message.