I have decided to take this course with Guillaume after reading the positive reviews about him here and even though I ended up getting an A in the course, I do not recommend taking this class with him. Guillaume is a nice guy overall, he makes jokes in class here and there but I couldn't understand anything from his classes. He writes and talks extremely fast and barely solves problems on the board, which makes the material seem very abstract and hard to grasp, even though it isn't. I ended up studying everything on my own, reading from the textbook and watching videos online. Midway through the semester, the attendance dropped to about 10%-20%. His exams are difficult and very technical. On the first midterm the mean was 32/50 I got a 31. On the second midterm the mean was 30/50 I got a 40, and on the final, the mean was 60/100 I got an 85. Like I said I ended up getting an A in the course. HW's are also pretty hard and are not similar to his exams. If you want to study for his exams, you should read the chapters in the textbook, solve the True/False questions, and solve the practice exams he hands out.
I feel as though I am fairly qualified to write a review for Barraquand as I have taken 3 semesters with him so far: Calc III, Linear and ODE. Over all, I think Guillaume is a great teacher in comparison to the rest of the math department. That being said, he is not the best teacher ever. GB is not the best teacher in terms of actual lectures. He sometimes goes on tangents of proofs which are albeit interesting not really relevant to the class. That being said, when discussing actual content he is fairly clear on what to expect and how to approach most problems. In linear particular he was a little confusing, but that was perhaps due to the subject matter rather than himself. His classes are somewhat dry but enjoyable, he cracks a lot of jokes and the class is fun. I think GB is an extremely fair teacher. All his HWs are very fair and his grading gives a lot of partial credit. His test, while difficult ask about the entire scope of the topic. They are very well made and really show if you understand the material. His curves are very generous, the last commenter was accurate in terms of grading. Moreover, since the tests are difficult and the averages are usually in the 50s-60s, getting a good grade is a lot easier then meets the eye. I would gladly recommend him to any of my friends.
TLDR; Meh teacher. Generous grader. Good tests and homework are okay. You'll learn the fundamentals if you study. Take him if you're an engineer looking for a pretty easy A. Long Version: I'm really conflicted about my experience. I got an A in the class (barely missed the A+ cut off), but I don't feel like I learned much. Barraquand does interesting proofs in the class that are decently rigorous, but he doesn't really show how the concepts of linear algebra are applied or the beauty of it. For example, isomorphisms are apparently really important, but he just mumbled some definitions without much geometric interpretation. Have no idea how to prove it or why I should care even though it seems cool. So I didn't learn how to do real proofs or learn how linear algebra is useful. Thus his class is a bit boring and attendance really dropped to 20% after the first few classes. Be prepared to study a lot and understand the material by yourself. His tests are actually really fair, interesting, and do a decent job of testing your grasp on the fundamentals. There are usually some true/false questions that aren't very hard if you think about them (kinda fun in reality), a few easy computational problems, and then some very long derivations/proofs. The derivation and proofs would be hard if he didn't walk you through them (e.g writing something like "hint, use a laplace expansion on the first row). His practice tests are similar/slightly harder than the actual midterm/final. The final would have been annoying if it weren't for his generous grading and partial credit. I was really bad at multiplying matrices so I had to use variables for some final results. Still scored well above the average despite that fact I screwed up most of the matrix multiplication. Homework was alright. Not too hard if you think about them. Grading was really erratic though. I always checked my homework with a friend, and we had the exact same answers (yes I showed my work). We often got very different grades.
Barraquand is a less than stellar teacher. He speaks in French-English, talks directly to the board, and takes notes right out of the textbook like you could do yourself. He likes to make up homework and exam questions that are either insanely difficult or don't have actual solutions. His written homework problems confused the TAs and himself at times. Right before midterms and the exam he taught us crazy concepts that never showed up anywhere in the course, and would often give one section much harder questions than the other on midterms. He provides one practice midterm for each midterm and one practice final, all of which have questions that he later deems "too difficult" during in-class review. Avoid Barraquand at all costs for Calc III.