Rating: 
Summary: Better proofs and clearer explanations are needed
Review: When I was a second-year math student, I found that "Vector Calculus" needed to provide students with clearer and more rigorous explanations and proofs of theorems. Too many statements were expected to be belived on face value. Specifically, I found no intuitive justification for the Jacobian Matrix anywhere in the book, nor any hint of a proof or explanation of its origins. Students will take to this already-challenging subject more if theorems are rigorously proved. This way they feel they're being treated like mathematicians instead of idiots. Moreover, the subject of multivariate calculus would feel like mathematics instead of a course in vocabulary memorization.
Rating:
Summary: Not a good intro.
Review: While some of my peers deem "Vector Calculus" to be a fine integration of theory and practice, I'd have to COMPLETELY disagree. From a teaching stand point, it is one of the worst texts out there (at least for a first course). At my university, some of the instructors have tried to use it as the text for the second half of a four quarter calculus sequence. This attempt has met with terrible failure, in my opinion. Most of my students (math majors and engineering students) found the book difficult and perplexing with few examples that pertained to the material they were required to learn. Luckily, the professor for my course was very good at conveying the ideas present without alluding to the text; nevertheless, I spent countless hours in discussion helping my students understand material that most standard texts would have clearly elucidated for them. In fact, at numerous points, the text becomes so involved with its own pedagogy that it neglects to delinate between important, must-know theorems and simply interesting facts. In addition, only the very first exercises in a given section are useful for most students. A number of the later questions become interesting problems in some upper div. class, but have no bearing on the course at hand. Quite a few of them are not difficult but require "tricks" which often discourage the students by giving them the impression that they don't get the material simply because they couldn't come up with the solutions to these extraneous questions. I would strongly recommend Stewart's text (for those of you on the West Coast) and Salas and Hille's text (for those of you in the Southwest). Prehaps, Marsden's text would be o.k. for a more advanced course on vector calc. or as a go-between supplement for a more rigorous text.
Rating:
Summary: Not a good intro.
Review: While some of my peers deem "Vector Calculus" to be a fine integration of theory and practice, I'd have to COMPLETELY disagree. From a teaching stand point, it is one of the worst texts out there (at least for a first course). At my university, some of the instructors have tried to use it as the text for the second half of a four quarter calculus sequence. This attempt has met with terrible failure, in my opinion. Most of my students (math majors and engineering students) found the book difficult and perplexing with few examples that pertained to the material they were required to learn. Luckily, the professor for my course was very good at conveying the ideas present without alluding to the text; nevertheless, I spent countless hours in discussion helping my students understand material that most standard texts would have clearly elucidated for them. In fact, at numerous points, the text becomes so involved with its own pedagogy that it neglects to delinate between important, must-know theorems and simply interesting facts. In addition, only the very first exercises in a given section are useful for most students. A number of the later questions become interesting problems in some upper div. class, but have no bearing on the course at hand. Quite a few of them are not difficult but require "tricks" which often discourage the students by giving them the impression that they don't get the material simply because they couldn't come up with the solutions to these extraneous questions. I would strongly recommend Stewart's text (for those of you on the West Coast) and Salas and Hille's text (for those of you in the Southwest). Prehaps, Marsden's text would be o.k. for a more advanced course on vector calc. or as a go-between supplement for a more rigorous text.
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