Multivariable Calculus for GRE?

Question

This is going to sound strange, but I am a third year math major who never took multivariable calculus (despite having taken courses on Galois and Lebesgue theory, etc). I plan to take the GRE next year and need to learn multivariable calculus (and analysis) over the summer. **What are some good textbooks for a quick crash course on multivariable calculus that would be germane to the GRE Subject Exam?** Edit: How about [this book](http://www.amazon.com/Multivariate-Calculus-Geometry-Undergraduate-Mathematics/dp/185233472X), for example? [Regarding its reviews](http://www.abstrusegoose.com/527) Edit 2: I have a pretty solid grasp of undergraduate linear algebra (having taken two courses in linear algebra and TAing the lower level course of the two). As such, the book may assume linear algebra as a prerequisite.

Answer 1

If you are talking about the GRE general exam, then don't worry about multivariate calculus. The mathematics portion of the general GRE has very similar questions and subjects as those found on the SAT or ACT mathematics portions.

For the mathematics subject GRE I would recommend starting your study by picking up a book focused on that particular test. I have taken the exam twice (once to get into a mathematics master program, again to get into a mathematics and science education PhD program). The questions are focused on being able to see the big ideas from the standard undergraduate mathematics courses and understand their applications. Most textbooks or crash courses are going to focus less on those big picture patterns and more on specific problems.

I would take a practice exam to get a feel for the types of questions that will be asked: multiple choice problems that are looking for conceptual and intuitive understandings rather than the ability to do computations (there simply isn't time during the exam to do everything by actual computations). I would then focus on the big picture ideas in multivariable calculus or any other area/course where you struggled on the exam.

When I took the exam, I recognized that I am just not great at intuitive understandings of differential equations. I can do the computations, but I just don't "see" the patterns like I am able to in analysis, abstract algebra, or number theory. In taking the exam, I simply skipped those problems and came back to them as I had time - and yes, both times I ran out of time. Realize that it takes a relatively low number of correct answers to do quite well on the exam. In past versions, correct answers on 40 out of 66 questions would put you in the 70th+ percentile with a scaled score well over the 700 that a large number of schools use as a cut-off.