I've been fortunate enough to have a series of great professors in the Chemistry Department. I'm happy to say I can add Professor Berne to this list. I thought by the end of it that I had a solid introduction to the discipline that is Physical Chemistry.
Pre-requisites: General Chemistry (of course). Although the course requires Physics I and II as pre-reqs, I don't feel as though we went beyond using F=ma. Calculus I,II,III are needed. There aren't many difficult integrations (except in Stat Mech) in the course however you should feel comfortable with partial derivatives as they are used frequently throughout the course.
Course: Physical Chemistry I covers Thermodynamics, Kinetics, and some statistical mechanics. It begins by exploring whether or not a reaction will occur spontaneously and then moves into how fast a reaction will occur. Some of this is very reminiscent of general chemistry, only taken a step further and thus more in depth. The class concludes with statistical mechanics (partition functions, the canonical ensemble, etc.) and used to derive the equations used throughout the course. Overall, it was an enjoyable subject mater. I found myself saying "this is cool" and "I love pchem" throughout this course.
Class (Professor Berne): Class was very useful to attend. Professor Berne was always enthusiastic about the material he was teaching and as a result I never really lost interest in the subject matter (he throws in humor periodically which i genuinely found funny). He is very clear with his notes on the board and goes at a reasonable pace. Furthermore, he would always make sure to answer any questions before moving on to the following topic. The only time I was at a complete loss was around Statistical Mechanics. It's more of a fault of the subject matter itself than Professor Berne as you really need to work out the math and derivations on your own to really understand it. This is when attending class is indispensable as I found that the lecture did a better job than the textbook when handling the subject. In regard to the reviews below, professor Berne only used power point maybe once in our class (understandably as the diagrams used would be heard to re-create by hand). He makes them available on coursework as a supplement rather than a required reading. Overall, Professor Berne is funny, concise, and excellent lecturer.
Recitation (TA Matt Mayers): Best TA at Columbia, but I'll be brief. Matt took the time to type out ALL of the class notes and made them available to the students. His recitations were helpful in clearing up any confusion and as a result were worth attending. Definitely made PCHEM less painful than it probably should have been.
Midterm: Actually a Mid-Term. It covers all of thermodynamics (minus electrochem). The questions were related to assigned HW problems and topics covered in depth in lecture. Overall they were reasonable albeit a bit lengthy.
No formula sheet. Probably one of the few things I disliked only because effort was put into memorizing them rather than being able to apply them.
Final Exam: The final exam was split into two tests. Test 1 spanned the whole course. Test 2 covered material after the midterm only. Pretty long so you may want to focus on one test first rather than jumping from one to the other. See Workload for more info.