I am interested in taking multivariable calculus (MAT237) at UT but need to know if I have the neccessary knowledge to succeed in it. I have taken only "Calculus for Life Sci" (MAT135) but achieved a high A in it. The course covers everything from contunity to infinite series, but omits mostly all the proofs. I found the course super easy except for maybe the formal limit definition (which I still dont fully grasp) as well as IVT and MVT theorems and proofs. So I have a very good intuitive knowledge of single variable calculus, but don't know many of the theorems or how to prove them. My primitive guess is they will be repeated in the general or multivariable case, so that this wont hurt. I got a taste of rigor with linear algebra, which was harsh at first but got better over time (although I still don't find many of the proofs convincing). Anyways, this advanced course uses Folland's Advanced Calculus and and covers the following topics: Euclidean Spaces and Vectors, Subsets of Euclidean Space, Limits and Continuity, Sequences, Completeness, Compactness, Connectedness, Uniform Continuity; Differential Calculus; Implicit Function theorem and applications; integral calculus; line and surface integrals with vector analysis; infinite series. I have also never heard of any of the "hard theorems" or any applications of IVT. This course is rated hard by colleagues, and requires advanced calculus from year 1 or a high grade in life sci calculus (which I have). So with this kind of foundation, am I ready to take on Folland? Or should I just dumb it down to life sci calc II ? Or should I take advanced single variable calc simultaneously with multi?