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Dr. Watson has a good sense of humor and is really nice and great at explaining concepts. That being said, his class (Fall 2012) was a nightmare, and I even took calc in high school and just wanted this as a refresher course. His homework was easy, as were the section quizzes, I studied hard for the midterms, really knew the stuff cold, and had he actually tested us on the class material, I would have had no problems. However, he tested us on theoretical math instead, which is totally different from the applied math (with some theory) he taught. After we got back the first midterm, he said that he was "disappointed" that 65% (it was probably more, but I don't remember) of the class failed. 65%! (And the 35% that passed probably didn't all get A's either.) He also said that he got lots of complaints about it, but "this is college, not high school." Then the second midterm was just as bad, so I dropped the class so I wouldn't fail and mess up my GPA.
I know that this is only one out of several reviews, but unless he's since revised his testing scheme or you're a theory-breathing genius, DO NOT take his class. Don't kill yourself and your GPA. Take someone reasonable instead.
Watson's lectures contained many proofs and explanations of concepts. In addition, he would sometimes explain certain concepts in great detail and not explain others at all (implicit differentiation). A good professor, but his personality and his office hours could be improved upon.
He is definitely a decent professor. Lectures are very organized and well-explained. Yes he does teach about the proofs and shows how to get from A to B, but isn't math supposed to teach you reasoning? Plus, he doesn't test you on them. Take him if you have the chance!
I found Watson to be pretty unapproachable. He blew me off when I asked if he knew of any good tutors. Lectures were sometimes decent, sometimes pointless, His tests don't look like his homework at all. If you don't mind being taught entirely in proofs and concepts, take Watson. Otherwise I would suggest avoiding him.